We consider a continuous-time game-theoretic model of an investment market with short-lived assets and endogenous asset prices. The first goal of the paper is to formulate a stochastic equation which determines wealth processes of investors and to provide conditions for the existence of its solution. The second goal is to show that there exists a strategy such that the logarithm of the relative wealth of an investor who uses it is a submartingale regardless of the strategies of the other investors, and the relative wealth of any other essentially different strategy vanishes asymptotically. This strategy can be considered as an optimal growth portfolio in the model.

We propose an adaptive and explicit fourth-order Runge-Kutta-Fehlberg method coupled with a fourth-order compact scheme to solve the American put options problem. First, the free boundary problem is converted into a system of partial differential equations with a fixed domain by using logarithm transformation and taking additional derivatives. With the addition of an intermediate function with a fixed free boundary, a quadratic formula is derived to compute the velocity of the optimal exercise boundary analytically. As such, it enables us to employ fourth-order spatial and temporal discretization with Dirichlet boundary conditions for obtaining the numerical solution of the asset option, option Greeks, and the optimal exercise boundary. The advantage of the Runge-Kutta-Fehlberg method is based on error control and the adjustment of the time step to maintain the error at a certain threshold. By comparing with some existing methods in numerical experiments, it shows that the present method has a better performance in terms of computational speed and provides a more accurate solution.

We propose and analyze semidefinite relaxation based locational marginal prices (RLMPs) for real and reactive power in electricity markets. Our analysis reveals that when the non-convex economic dispatch problem has zero duality gap, the RLMPs exhibit properties similar to locational marginal prices with linearized power flow equations. Otherwise, they behave similar to convex hull prices. Restricted to radial distribution networks, RLMPs reduce to second-order cone relaxation based distribution locational marginal prices. We illustrate our theoretical results on numerical examples.

Every nation prioritizes the inclusive economic growth and development of all regions. However, we observe that economic activities are clustered in space, which results in a disparity in per-capita income among different regions. A complexity-based method was proposed by Hidalgo and Hausmann [PNAS 106, 10570-10575 (2009)] to explain the large gaps in per-capita income across countries. Although there have been extensive studies on countries' economic complexity using international export data, studies on economic complexity at the regional level are relatively less studied. Here, we study the industrial sector complexity of prefectures in Japan based on the basic information of more than one million firms. We aggregate the data as a bipartite network of prefectures and industrial sectors. We decompose the bipartite network as a prefecture-prefecture network and sector-sector network, which reveals the relationships among them. Similarities among the prefectures and among the sectors are measured using a metric. From these similarity matrices, we cluster the prefectures and sectors using the minimal spanning tree technique.The computed economic complexity index from the structure of the bipartite network shows a high correlation with macroeconomic indicators, such as per-capita gross prefectural product and prefectural income per person. We argue that this index reflects the present economic performance and hidden potential of the prefectures for future growth.

Disagreement is an essential element of science and life in general. The language of probabilities and statistics is often used to describe disagreements quantitatively. In practice, however, we want much more than that. We want disagreements to be resolved. This leaves us with a substantial knowledge gap which is often perceived as a lack of practical intuition regarding probabilistic and statistical concepts.

Take for instance the R\'enyi divergence which is a well-known statistical quantity specifically designed as a measure of disagreement between probabilistic models. Despite its widespread use in science and engineering, the R\'enyi divergence remains a highly abstract axiomatically-motivated measure. Certainly, it offers no practical insight as to how disagreements can be resolved.

Here we propose to address disagreements using the methods of financial economics. In particular, we show how a large class of disagreements can be transformed into investment opportunities. The expected financial performance of such investments quantifies the amount of disagreement in a tangible way. This provides intuition for statistical concepts such as the R\'enyi divergence which becomes connected to the financial performance of optimized investments. Investment optimization takes into account individual opinions as well as attitudes towards risk. The result is a market-like social mechanism by which funds flow naturally to support a more accurate view. Such social mechanisms can help us with difficult disagreements (e.g., financial arguments concerning the future climate).

In terms of scientific validation, we used the findings of independent neurophysiological experiments as well as our own research on the equity premium.

Recent studies concerning the point electricity price forecasting have shown evidence that the hourly German Intraday Continuous Market is weak-form efficient. Therefore, we take a novel, advanced approach to the problem. A probabilistic forecasting of the hourly intraday electricity prices is performed by simulating trajectories in every trading window to receive a realistic ensemble to allow for more efficient intraday trading and redispatch. A generalized additive model is fitted to the price differences with the assumption that they follow a zero-inflated distribution, precisely a mixture of the Dirac and the Student's t-distributions. Moreover, the mixing term is estimated using a high-dimensional logistic regression with lasso penalty. We model the expected value and volatility of the series using i.a. autoregressive and no-trade effects or load, wind and solar generation forecasts and accounting for the non-linearities in e.g. time to maturity. Both the in-sample characteristics and forecasting performance are analysed using a rolling window forecasting study. Multiple versions of the model are compared to several benchmark models and evaluated using probabilistic forecasting measures and significance tests. The study aims to forecast the price distribution in the German Intraday Continuous Market in the last 3 hours of trading, but the approach allows for application to other continuous markets, especially in Europe. The results prove superiority of the mixture model over the benchmarks gaining the most from the modelling of the volatility. They also indicate that the introduction of XBID reduced the market volatility.

Failure to receive post-natal care within first week of delivery causes a 3% increase in the possibility of Acute Respiratory Infection in children under five. Mothers with unpaid maternity leave put their children at a risk of 3.9% increase in the possibility of ARI compared to those with paid maternity leave.

We propose kernel-based collocation methods for numerical solutions to Heath-Jarrow-Morton models with Musiela parametrization. The methods can be seen as the Euler-Maruyama approximation of some finite dimensional stochastic differential equations, and allow us to compute the derivative prices by the usual Monte Carlo methods. We derive a bound on the rate of convergence under some decay condition on the inverse of the interpolation matrix and some regularity conditions on the volatility functionals.

We introduce a simulation method for dynamic portfolio valuation and risk management building on machine learning with kernels. We learn the dynamic value process of a portfolio from a finite sample of its cumulative cash flow. The learned value process is given in closed form thanks to a suitable choice of the kernel. We show asymptotic consistency and derive finite sample error bounds under conditions that are suitable for finance applications. Numerical experiments show good results in large dimensions for a moderate training sample size.

This article studies the impact of carbon risk on stock pricing. To address this, we consider the seminal approach of G\"orgen \textsl{et al.} (2019), who proposed estimating the carbon financial risk of equities by their carbon beta. To achieve this, the primary task is to develop a brown-minus-green (or BMG) risk factor, similar to Fama and French (1992). Secondly, we must estimate the carbon beta using a multi-factor model. While G\"orgen \textsl{et al.} (2019) considered that the carbon beta is constant, we propose a time-varying estimation model to assess the dynamics of the carbon risk. Moreover, we test several specifications of the BMG factor to understand which climate change-related dimensions are priced in by the stock market. In the second part of the article, we focus on the carbon risk management of investment portfolios. First, we analyze how carbon risk impacts the construction of a minimum variance portfolio. As the goal of this portfolio is to reduce unrewarded financial risks of an investment, incorporating the carbon risk into this approach fulfils this objective. Second, we propose a new framework for building enhanced index portfolios with a lower exposure to carbon risk than capitalization-weighted stock indices. Finally, we explore how carbon sensitivities can improve the robustness of factor investing portfolios.

Asian option, as one of the path-dependent exotic options, is widely traded in the energy market, either for speculation or hedging. However, it is hard to price, especially the one with the arithmetic average price. The traditional trading procedure is either too restrictive by assuming the distribution of the underlying asset or less rigorous by using the approximation. It is attractive to infer the Asian option price with few assumptions of the underlying asset distribution and adopt to the historical data with a nonparametric method. In this paper, we present a novel approach to price the Asian option from an imprecise statistical aspect. Nonparametric Predictive Inference (NPI) is applied to infer the average value of the future underlying asset price, which attempts to make the prediction reflecting more uncertainty because of the limited information. A rational pairwise trading criterion is also proposed in this paper for the Asian options comparison, as a risk measure. The NPI method for the Asian option is illustrated in several examples by using the simulation techniques or the empirical data from the energy market.

Financial markets provide a natural quantitative lab for understanding some of the most advanced human behaviours. Among them is the use of mathematical tools known as financial instruments. Besides money, the two most fundamental financial instruments are bonds and equities. More than 30 years ago Mehra and Prescott found the numerical performance of equities relative to government bonds could not be explained by consumption-based (mainstream) economic theories. This empirical observation, known as the Equity Premium Puzzle, has been defying mainstream economics ever since. The recent financial crisis revealed an even deeper need for understanding financial products. We show how understanding the rational nature of product design resolves the Equity Premium Puzzle. In doing so we obtain an experimentally tested theory of product design.

Most of the existing literature on the current pandemic focuses on approaches to model the outbreak and spreading of COVID-19. This paper proposes a generalized Markov-Switching approach, the SUIHR model, designed to study border control policies and contact tracing against COVID-19 in a period where countries start to re-open. We offer the following contributions. First, the SUIHR model can include multiple entities, reflecting different government bodies with different containment measures. Second, constraints as, for example, new case targets and medical resource limits can be imposed in a linear programming framework. Third, in contrast to most SIR models, we focus on the spreading of infectious people without symptoms instead of the spreading of people who are already showing symptoms. We find that even if a country has closed its borders completely, domestic contact tracing is not enough to go back to normal life. Countries having successfully controlled the virus can keep it under check as long as imported risk is not growing, meaning they can lift travel restrictions with similar countries. However, opening borders towards countries with less controlled infection dynamics would require a mandatory quarantine or a strict test on arrival.

Nested simulation arises frequently in financial or input uncertainty quantification problems, where the performance measure is defined as a function of the simulation output mean conditional on the outer scenario. The standard nested simulation samples $M$ outer scenarios and runs $N$ inner replications at each. We propose a new experiment design framework for a problem whose inner replication's inputs are generated from probability distribution functions parameterized by the outer scenario. This structure lets us pool replications from an outer scenario to estimate another scenario's conditional mean via the likelihood ratio method. We formulate a bi-level optimization problem to decide not only which of $M$ outer scenarios to simulate and how many times to replicate at each, but also how to pool these replications such that the total simulation effort is minimized while achieving the same estimation error as the standard nested simulation. The resulting optimal design requires far less simulation effort than $MN$. We provide asymptotic analyses on the convergence rates of the performance measure estimators computed from the experiment design. Empirical results show that our experiment design significantly reduces the simulation cost compared to the standard nested simulation as well as a state-of-the-art design that pools replications via regressions.

In behavioural economics, a decision maker's preferences are expressed by choice functions. Preference robust optimization(PRO) is concerned with problems where the decision maker's preferences are ambiguous, and the optimal decision is based on a robust choice function with respect to a preference ambiguity set. In this paper, we propose a PRO model to support choice functions that are: (i) monotonic (prefer more to less), (ii) quasi-concave (prefer diversification), and (iii) multi-attribute (have multiple objectives/criteria). As our main result, we show that the robust choice function can be constructed efficiently by solving a sequence of linear programming problems. Then, the robust choice function can be optimized efficiently by solving a sequence of convex optimization problems. Our numerical experiments for the portfolio optimization and capital allocation problems show that our method is practical and scalable.

The paper is a collection of knowledge regarding the phenomenon of climate change, competitiveness, and literature linking the two phenomena to agricultural market competitiveness. The objective is to investigate the peer reviewed and grey literature on the subject to explore the link between climate change and agricultural market competitiveness and also explore an appropriate technique to validate the presumed relationship empirically. The paper concludes by identifying implications for developing an agricultural competitiveness index while incorporating the climate change impacts, to enhance the potential of agricultural markets for optimizing the agricultural sectors competitiveness.

In this paper, we aim at solving the cardinality constrained high-order portfolio optimization, i.e., mean-variance-skewness-kurtosis model with cardinality constraint (MVSKC). Optimization for the MVSKC model is of great difficulty in two parts. One is that the objective function is non-convex, the other is the combinational nature of the cardinality constraint, leading to non-convexity as well dis-continuity. Based on the observation that cardinality constraint has the difference-of-convex (DC) property, we transform the cardinality constraint into a penalty term and then propose three algorithms including the proximal difference of convex algorithm (pDCA), pDCA with extrapolation (pDCAe) and the successive convex approximation (SCA) to handle the resulting penalized MVSK (PMVSK) formulation. Moreover, theoretical convergence results of these algorithms are established respectively. Numerical experiments on the real datasets demonstrate the superiority of our proposed methods in obtaining high utility and sparse solutions as well as efficiency in terms of time usage.

We presented Bayesian portfolio selection strategy, via the $k$ factor asset pricing model. If the market is information efficient, the proposed strategy will mimic the market; otherwise, the strategy will outperform the market. The strategy depends on the selection of a portfolio via Bayesian multiple testing methodologies. We present the "discrete-mixture prior" model and the "hierarchical Bayes model with horseshoe prior." We define the Oracle set and prove that asymptotically the Bayes rule attains the risk of Bayes Oracle up to $O(1)$. Our proposed Bayes Oracle test guarantees statistical power by providing the upper bound of the type-II error. Simulation study indicates that the proposed Bayes oracle test is suitable for the efficient market with few stocks inefficiently priced. However, as the model becomes dense, i.e., the market is highly inefficient, one should not use the Bayes oracle test. The statistical power of the Bayes Oracle portfolio is uniformly better for the $k$-factor model ($k>1$) than the one factor CAPM. We present the empirical study, where we considered the 500 constituent stocks of S\&P 500 from the New York Stock Exchange (NYSE), and S\&P 500 index as the benchmark for thirteen years from the year 2006 to 2018. We showed the out-sample risk and return performance of the four different portfolio selection strategies and compared with the S\&P 500 index as the benchmark market index. Empirical results indicate that it is possible to propose a strategy which can outperform the market.

This study aims to investigate the behavior of stock prices throughout the episodes of foreign capital flows using data of daily stock prices and quarterly foreign capital flows from 14 EMEs. To this end, the episodes of capital flows are identified using the threshold and the k-means clustering approaches. Next, the stock index changepoints are detected using the Pruned Exact Linear Time (PELT) method. Finally, we combine the results by distributing the detected changepoints over the identified capital flows. The results reveal that the stock indices have been rarely pushed further during the entire surge episodes identified by both approaches, and thus surges of capital flows do not necessarily lead to further appreciation of stock prices. In the meantime, a significant appreciation of stock prices is observed during the normal state of capital flows. On the other hand, it is noticed that the stock prices have not often depreciated during the episodes of foreign capital outflows in all the selected EMEs, which means that stock prices have been less vulnerable to reversals of foreign capital flows

Groups of enterprises can serve as guarantees for one another and form complex networks when obtaining loans from commercial banks. During economic slowdowns, corporate default may spread like a virus and lead to large-scale defaults or even systemic financial crises. To help financial regulatory authorities and banks manage the risk associated with networked loans, we identified the default contagion risk, a pivotal issue in developing preventive measures, and established iConVis, an interactive visual analysis tool that facilitates the closed-loop analysis process. A novel financial metric, the contagion effect, was formulated to quantify the infectious consequences of guarantee chains in this type of network. Based on this metric, we designed and implement a series of novel and coordinated views that address the analysis of financial problems. Experts evaluated the system using real-world financial data. The proposed approach grants practitioners the ability to avoid previous ad hoc analysis methodologies and extend coverage of the conventional Capital Accord to the banking industry.