Fundamental variables in financial market are not only price and return but a very important role is also played by trading volumes. Here we propose a new multivariate model that takes into account price returns, logarithmic variation of trading volumes and also waiting times, the latter to be intended as the time interval between changes in trades, price, and volume of stocks. Our approach is based on a generalization of semi-Markov chains where an endogenous index process is introduced. We also take into account the dependence structure between the above mentioned variables by means of copulae. The proposed model is motivated by empirical evidences which are known in financial literature and that are also confirmed in this work by analysing real data from Italian stock market in the period August 2015 - August 2017. By using Monte Carlo simulations, we show that the model reproduces all these empirical evidences.

Aiming for more realistic optimal dividend policies, we consider a stochastic control problem with linearly bounded control rates using a performance function given by the expected present value of dividend payments made up to ruin. In a Brownian model, we prove the optimality of a member of a new family of control strategies called delayed linear control strategies, for which the controlled process is a refracted diffusion process. For some parameters specifications, we retrieve the strategy initially proposed by Avanzi & Wong (2012) to regularize dividend payments, which is more consistent with actual practice.

Financial time-series analysis and forecasting have been extensively studied over the past decades, yet still remain as a very challenging research topic. Since the financial market is inherently noisy and stochastic, a majority of financial time-series of interests are non-stationary, and often obtained from different modalities. This property presents great challenges and can significantly affect the performance of the subsequent analysis/forecasting steps. Recently, the Temporal Attention augmented Bilinear Layer (TABL) has shown great performances in tackling financial forecasting problems. In this paper, by taking into account the nature of bilinear projections in TABL networks, we propose Bilinear Normalization (BiN), a simple, yet efficient normalization layer to be incorporated into TABL networks to tackle potential problems posed by non-stationarity and multimodalities in the input series. Our experiments using a large scale Limit Order Book (LOB) consisting of more than 4 million order events show that BiN-TABL outperforms TABL networks using other state-of-the-arts normalization schemes by a large margin.

In this short note we develop a model for discounting.

A focus of the model is the discounting, when discount factors cannot be derived from market products. That is, a risk-neutralizing trading strategy cannot be performed.

This is the case, when one is in need of a risk-free (default-free) discounting, but default protection on funding providers is not traded. For this case, we introduce a default compensation factor ($\exp(+\tilde{\lambda} T)$) that describes the present value of a strategy to compensate for default (like buying default protection would do).

In a second part, we introduce a model, where the survival probability depends on the required notional. This model is different from the classical modelling of a time-dependent survival probability ($\exp(-\lambda T)$). The model especially allows that large liquidity requirements are instantly more likely do default than small ones.

Combined the two approaches build a framework in which discounting (valuation) is non-linear.

The framework can lead to the effect that discount-factors for very large liquidity requirements or projects are an increasing function of time.

Higher life expectancy and rapidly aging populations in developing countries, especially in the last three decades, have created the need for policymakers to introduce pension programs in developing countries. China launched the New Rural Pension Scheme (NRPS) in 2009 to ease internal demographic pressures and concerns about old-age poverty. Using data from the introduction of the NRPS in China, we estimate the effects of pension benefits, due to participation in the NRPS, on individual cognition, measured by episodic memory and intact mental status, among individuals aged 60 and above. We find large negative effects of the provision of pension benefits on cognitive functioning among the elderly. We detect the most substantial impact of the program to be on delayed recall, a measure implicated in neurobiological research as a significant predictor of the onset of dementia. We show suggestive evidence that the program leads to stronger negative impacts among the female sample. Our findings support the mental retirement hypothesis, that decreased mental activity results in atrophy of cognitive skills. We show that retirement plays a significant role in explaining cognitive decline at older ages.

Ride-hailing marketplaces like Uber and Lyft use dynamic pricing, often called surge, to balance the supply of available drivers with the demand for rides. We study driver-side payment mechanisms for such marketplaces, presenting the theoretical foundation that has informed the design of Uber's new additive driver surge mechanism. We present a dynamic stochastic model to capture the impact of surge pricing on driver earnings and their strategies to maximize such earnings. In this setting, some time periods (surge) are more valuable than others (non-surge), and so trips of different time lengths vary in the induced driver opportunity cost.

First, we show that multiplicative surge, historically the standard on ride-hailing platforms, is not incentive compatible in a dynamic setting. We then propose a structured, incentive-compatible pricing mechanism. This closed-form mechanism has a simple form and is well-approximated by Uber's new additive surge mechanism. Finally, through both numerical analysis and real data from a ride-hailing marketplace, we show that additive surge is more incentive compatible in practice than is multiplicative surge.

This paper examines the pricing of short-term and long-term dynamic network risk in the cross-section of stock returns. Stocks with high sensitivities to dynamic network risk earn lower returns. We rationalize our finding with economic theory that allows the stochastic discount factor to load on network risk through the precautionary savings channel. A one-standard deviation increase in long-term (short-term) network risk loadings associate with a 7.66% (6.71%) drop in annualized expected returns.

The rank-size plots of a large number of different physical and socio-economic systems are usually said to follow Zipf's law, but a unique framework for the comprehension of this ubiquitous scaling law is still lacking. Here we show that a dynamical approach is crucial: during their evolution, some systems are attracted towards Zipf's law, while others presents Zipf's law only temporarily and, therefore, spuriously. A truly Zipfian dynamics is characterized by a dynamical constraint, or coherence, among the parameters of the generating PDF, and the number of elements in the system. A clear-cut example of such coherence is natural language. Our framework allows us to derive some quantitative results that go well beyond the usual Zipf's law: i) earthquakes can evolve only incoherently and thus show Zipf's law spuriously; this allows an assessment of the largest possible magnitude of an earthquake occurring in a geographical region. ii) We prove that Zipfian dynamics are not additive, explaining analytically why US cities evolve coherently, while world cities do not. iii) Our concept of coherence can be used for model selection, for example, the Yule-Simon process can describe the dynamics of world countries' GDP. iv) World cities present spurious Zipf's law and we use this property for estimating the maximal population of an urban agglomeration.

This paper quantifies the effects of equity tail risk on the US government bond market. We estimate equity tail risk with option-implied stock market volatility that stems from large negative price jumps, and we assess its value in reduced-form predictive regressions for Treasury returns and a term structure model for interest rates. We find that the left tail volatility of the stock market significantly predicts one-month excess returns on Treasuries both in- and out-of-sample. The incremental value of employing equity tail risk as a return forecasting factor can be of economic importance for a mean-variance investor trading bonds. The estimated term structure model shows that equity tail risk is priced in the US government bond market and, consistent with the theory of flight-to-safety, Treasury prices increase when the perception of tail risk is higher. Our results concerning the predictive power and pricing of equity tail risk extend to major government bond markets in Europe.

Modern technology and innovations are becoming more crucial than ever for the survival of companies in the market. Therefore, it is significant both from theoretical and practical points of view to understand how governments can influence technology growth and innovation diffusion (TGID) processes. We propose a simple but essential extension of Ausloos-Clippe-P\c{e}kalski and related Cichy numerical models of the TGID in the market. Both models are inspired by the nonlinear non-equilibrium statistical physics. Our extension involves a parameter describing the probability of government intervention in the TGID process in the company market. We show, using Monte Carlo simulations, the effects interventionism can have on the companies' market, depending on the segment of firms that are supported. The high intervention probability can result, paradoxically, in the destabilization of the market development. It lowers the market's technology level in the long-time limit compared to markets with a lower intervention parameter. We found that the intervention in the technologically weak and strong segments of the company market does not substantially influence the market dynamics, compared to the intervention helping the middle-level companies. However, this is still a simple model which can be extended further and made more realistic by including other factors. Namely, the cost and risk of innovation or limited government resources and capabilities to support companies.

We analyze actively managed mutual funds in China from 2005 to 2017. We develop performance measures for asset allocation and selection. We find that stock selection ability from holding-based model is positively correlated with selection ability estimated from Fama-French three-factor model, which is price-based regression model. We also find that industry allocation from holding-based model is positively correlated with timing ability estimated from price-based Treynor-Mazuy model most of the time. We conclude that most actively managed funds have positive stock selection ability but not asset allocation ability, which is due to the difficulty in predicting policy changes.

Several proposals for the reform of the euro area advocate the creation of a market in synthetic securities backed by portfolios of sovereign bonds. Most debated are the so-called European Safe Bonds or ESBies proposed by Brunnermeier, Langfield, Pagano,Reis, Van Nieuwerburgh and Vayanos (2017). The potential benefits of ESBies and other bond-backed securities hinge on the assertion that these products are really safe. In this paper we provide a comprehensive quantitative study of the risks associated with ESBies and related products, using an affine credit risk model with regime switching as vehicle for our analysis. We discuss a recent proposal of Standard and Poors for the rating of ESBies, we analyse the impact of model parameters and attachment points on the size and the volatility of the credit spread of ESBies and we consider several approaches to assess the market risk of ESBies. Moreover, we compare ESBies to synthetic securities created by pooling the senior tranche of national bonds as suggested by Leandro and Zettelmeyer(2019). The paper concludes with a brief discussion of the policy implications from our analysis.

The rapid rise of antibiotic resistance is a serious threat to global public health. Without further incentives, pharmaceutical companies have little interest in developing antibiotics, since the success probability is low and development costs are huge. The situation is exacerbated by the "antibiotics dilemma": Developing narrow-spectrum antibiotics against resistant bacteria is most beneficial for society, but least attractive for companies since their usage is more limited than for broad-spectrum drugs and thus sales are low. Starting from a general mathematical framework for the study of antibiotic-resistance dynamics with an arbitrary number of antibiotics, we identify efficient treatment protocols and introduce a market-based refunding scheme that incentivizes pharmaceutical companies to develop narrow-spectrum antibiotics: Successful companies can claim a refund from a newly established antibiotics fund that partially covers their development costs. The proposed refund involves a fixed and variable part. The latter (i) increases with the use of the new antibiotic for currently resistant strains in comparison with other newly developed antibiotics for this purpose---the resistance premium---and (ii) decreases with the use of this antibiotic for non-resistant bacteria. We outline how such a refunding scheme can solve the antibiotics dilemma and cope with various sources of uncertainty inherent in antibiotic R\&D. Finally, connecting our refunding approach to the recently established antimicrobial resistance (AMR) action fund, we discuss how the antibiotics fund can be financed.

Black-Scholes (BS) is the standard mathematical model for option pricing in financial markets. Option prices are calculated using an analytical formula whose main inputs are strike (at which price to exercise) and volatility. The BS framework assumes that volatility remains constant across all strikes, however, in practice it varies. How do traders come to learn these parameters? We introduce natural models of learning agents, in which they update their beliefs about the true implied volatility based on the opinions of other traders. We prove convergence of these opinion dynamics using techniques from control theory and leader-follower models, thus providing a resolution between theory and market practices. We allow for two different models, one with feedback and one with an unknown leader.

Under mean-variance-utility framework, we propose a new portfolio selection model, which allows wealth and time both have influences on risk aversion in the process of investment. We solved the model under a game theoretic framework and analytically derived the equilibrium investment (consumption) policy. The results conform with the facts that optimal investment strategy heavily depends on the investor's wealth and future income-consumption balance as well as the continuous optimally consumption process is highly dependent on the consumption preference of the investor.

What are the chances of an ethical individual rising through the ranks of a political party or a corporation in the presence of unethical peers? To answer this question, I consider a four-player two-stage elimination tournament, in which players are partitioned into those willing to be involved in sabotage behavior and those who are not. I show that, under certain conditions, the latter are more likely to win the tournament.

In this paper we present an asset allocation strategy based on the maximization of the Sortino ratio. Unlike the Sharpe ratio, the Sortino ratio penalizes negative return variances only. The resulting allocation is valid for any time horizon unlike. The returns of a strategy based on such an allocation are empirically illustrated using historical Dow Jones data and display a significant upgrade on more traditional allocation strategies such as the Kelly criterion.

We provide analytical results for a static portfolio optimization problem with two coherent risk measures. The use of two risk measures is motivated by joint decision-making for portfolio selection where the risk perception of the portfolio manager is of primary concern, hence, it appears in the objective function, and the risk perception of an external authority needs to be taken into account as well, which appears in the form of a risk constraint. The problem covers the risk minimization problem with an expected return constraint and the expected return maximization problem with a risk constraint, as special cases. For the general case of an arbitrary joint distribution for the asset returns, under certain conditions, we characterize the optimal portfolio as the optimal Lagrange multiplier associated to an equality-constrained dual problem. Then, we consider the special case of Gaussian returns for which it is possible to identify all cases where an optimal solution exists and to give an explicit formula for the optimal portfolio whenever it exists.

This paper enhances the pricing of derivatives as well as optimal control problems to a level comprising risk. We employ nested risk measures to quantify risk, investigate the limiting behavior of nested risk measures within the classical models in finance and characterize existence of the risk-averse limit. As a result we demonstrate that the nested limit is unique, irrespective of the initially chosen risk measure. Within the classical models risk aversion gives rise to a stream of risk premiums, comparable to dividend payments. In this context we connect coherent risk measures with the Sharpe ratio from modern portfolio theory and extract the Z-spread -- a widely accepted quantity in economics to hedge risk. The results for European option pricing are then extended to risk-averse American options, where we study the impact of risk on the price as well as the optimal time to exercise the option. We also extend Merton's optimal consumption problem to the risk-averse setting.

Income inequality between different races in the U.S. is especially large. This difference is even larger when gender is involved. In a complementary study, we have developed a dynamic microeconomic model accurately describing the evolution of male and female incomes since 1930. Here, we extend our analysis and model the disparity between black and white population in the U.S., separately for males and females. Unfortunately, income microdata provided by the U.S. Census Bureau for other races and ethnic groups are not time compatible or too short for modelling purposes. We are forced to constrain our analysis to black and white population, but all principal results can be extrapolated to other races and ethnicities. Our analysis shows that black females and white males are two poles of the overall income inequality. The prediction of income distribution for two extreme cases with one model is the main challenge of this study.

In this paper we introduce a numerical method for optimal stopping in the framework of one dimensional diffusion. We use the Skorokhod embedding in order to construct recombining tree approximations for diffusions with general coefficients. This technique allows us to determine convergence rates and construct nearly optimal stopping times which are optimal at the same rate. Finally, we demonstrate the efficiency of our scheme with several examples of game options.

The Pakistan competition policy, as in many other countries, was originally designed to regulate business conduct in traditional markets and for tangible goods and services. However, the development and proliferation of the internet has led to the emergence of digital companies which have disrupted many sectors of the economy. These platforms provide digital infrastructure for a range of services including search engines, marketplaces, and social networking sites. The digital economy poses a myriad of challenges for competition authorities worldwide, especially with regard to digital mergers and acquisitions (M&As). While some jurisdictions such as the European Union and the United States have taken significant strides in regulating technological M&As, there is an increasing need for developing countries such as Pakistan to rethink their competition policy tools. This paper investigates whether merger reviews in the Pakistan digital market are informed by the same explanatory variables as in the traditional market, by performing an empirical comparative analysis of the Competition Commission of Pakistan's (CCP's) M&A decisions between 2014 and 2019. The findings indicate the CCP applies the same decision factors in reviewing both traditional and digital M&As. As such, this paper establishes a basis for igniting the policy and economic debate of regulating the digital platform industry in Pakistan.

We introduce time-inhomogeneous stochastic volatility models, in which the volatility is described by a nonnegative function of a Volterra type continuous Gaussian process that may have very rough sample paths. The main results obtained in the paper are sample path and small-noise large deviation principles for the log-price process in a time-inhomogeneous super rough Gaussian model under very mild restrictions. We use these results to study the asymptotic behavior of binary barrier options, exit time probability functions, and call options.

We propose a modification of the classical Black-Derman-Toy (BDT) interest rate tree model, which includes the possibility of a jump with small probability at each step to a practically zero interest rate. The corresponding BDT algorithms are consequently modified to calibrate the tree containing the zero interest rate scenarios. This modification is motivated by the recent 2008-2009 crisis in the United States and it quantifies the risk of a future crises in bond prices and derivatives. The proposed model is useful to price derivatives. This exercise also provides a tool to calibrate the probability of this event. A comparison of option prices and implied volatilities on US Treasury bonds computed with both the proposed and the classical tree model is provided, in six different scenarios along the different periods comprising the years 2002-2017.