We price European-style options written on forward contracts in a commodity market, which we model with a state-dependent infinite-dimensional Heath-Jarrow-Morton (HJM) approach. We introduce a new class of volatility operators which map the square integrable noise into the Filipovi\'{c} space of forward curves, and we specify a deterministic parametrized version of it. For calibration purposes, we train a neural network to approximate the option price as a function of the model parameters. We then use it to calibrate the HJM parameters starting from (simulated) option market data. Finally we introduce a new loss function that takes into account bid and ask prices and offers a solution to calibration in illiquid markets. A key issue discovered is that the trained neural network might be non-injective, which could potentially lead to poor accuracy in calibrating the forward curve parameters, even when showing a high degree of accuracy in recovering the prices. This reveals that the original meaning of the parameters gets somehow lost in the approximation.

The Quasi-Maximum Likelihood (QML) procedure is widely used for statistical inference due to its robustness against overdisper-sion. However, while there are extensive references on non-recursive QML estimation, recursive QML estimation has attracted little attention until recently. In this paper, we investigate the convergence properties of the QML procedure in a general conditionally heteroscedastic time series model, extending the classical offline optimization routines to recursive approximation. We propose an adaptive recursive estimation routine for GARCH models using the technique of Variance Targeting Estimation (VTE) to alleviate the convergence difficulties encountered in the usual QML estimation. Finally, empirical results demonstrate a favorable trade-off between the ability to adapt to time-varying estimates and stability of the estimation routine.

During the COVID-19 pandemic of 2019/2020, authorities have used temporary \textit{ad-hoc} policy measures, such as lockdowns and mass quarantines, to slow its transmission. However, the consequences of widespread use of these unprecedented measures are poorly understood. To contribute to the understanding of the economic and human consequences of such policy measures, we therefore construct a mathematical model of an economy under the impact of a pandemic, select parameter values to represent the global economy under the impact of COVID-19, and perform numerical experiments by simulating a large number of possible policy responses. By varying the starting date of the policy intervention in the simulated scenarios, we find that the most effective policy intervention occurs around the time when the number of active infections is growing at its highest rate -- that is, the results suggest that the most dramatic measures should only be implemented when the disease is sufficiently spread. The degree of the intervention, above a certain threshold, does not appear to have a great impact on the outcomes in our simulations, due to the strongly concave relationship we assume between production shortfall and reduction in the infection rate. Our experiments further suggest that the intervention should last until after the peak determined by the reduced infection rate. The model and its implementation, along with the general insights from our policy experiments, may help policymakers design effective emergency policy responses in the face a serious pandemic, and contribute to our understanding of the relationship between the economic growth and the spread of infectious diseases.

We study portfolio selection in a complete continuous-time market where the preference is dictated by the rank-dependent utility. As such a model is inherently time inconsistent due to the underlying probability weighting, we study the investment behavior of sophisticated consistent planners who seek (subgame perfect) intra-personal equilibrium strategies. We provide sufficient conditions under which an equilibrium strategy is a replicating portfolio of a final wealth. We derive this final wealth profile explicitly, which turns out to be in the same form as in the classical Merton model with the market price of risk process properly scaled by a deterministic function in time. We present this scaling function explicitly through the solution to a highly nonlinear and singular ordinary differential equation, whose existence of solutions is established. Finally, we give a necessary and sufficient condition for the scaling function to be smaller than 1 corresponding to an effective reduction in risk premium due to probability weighting.

Attitudes toward risk underlie virtually every important economic decision an individual makes. In this experimental study, I examine how introducing a time delay into the execution of an investment plan influences individuals' risk preferences. The field experiment proceeded in three stages: a decision stage, an execution stage and a payout stage. At the outset, in the Decision Stage (Stage 1), each subject was asked to make an investment plan by splitting a monetary investment amount between a risky asset and a safe asset. Subjects were informed that the investment plans they made in the Decision Stage are binding and will be executed during the Execution Stage (Stage 2). The Payout Stage (Stage 3) was the payout date. The timing of the Decision Stage and Payout Stage was the same for each subject, but the timing of the Execution Stage varied experimentally. I find that individuals who were assigned to execute their investment plans later (i.e., for whom there was a greater delay prior to the Execution Stage) invested a greater amount in the risky asset during the Decision Stage.

This paper introduces a new functional optimization approach to portfolio optimization problems by treating the unknown weight vector as a function of past values instead of treating them as fixed unknown coefficients in the majority of studies. We first show that the optimal solution, in general, is not a constant function. We give the optimal conditions for a vector function to be the solution, and hence give the conditions for a plug-in solution (replacing the unknown mean and variance by certain estimates based on past values) to be optimal. After showing that the plug-in solutions are sub-optimal in general, we propose gradient-ascent algorithms to solve the functional optimization for mean-variance portfolio management with theorems for convergence provided. Simulations and empirical studies show that our approach can perform significantly better than the plug-in approach.

We present an alternative formula to price European options through cosine series expansions, under models with a known characteristic function such as the Heston stochastic volatility model. It is more robust across strikes and as fast as the original COS method.

The X-valuation adjustment (XVA) problem, which is a recent topic in mathematical finance, is considered and analyzed. First, the basic properties of backward stochastic differential equations (BSDEs) with a random horizon in a progressively enlarged filtration are reviewed. Next, the pricing/hedging problem for defaultable over-the-counter (OTC) derivative securities is described using such BSDEs. An explicit sufficient condition is given to ensure the non-existence of an arbitrage opportunity for both the seller and buyer of the derivative securities. Furthermore, an explicit pricing formula is presented in which XVA is interpreted as approximated correction terms of the theoretical fair price.

This paper is concerned with an optimal reinsurance and investment problem for an insurance firm under the criterion of mean-variance. The driving Brownian motion and the rate in return of the risky asset price dynamic equation cannot be directly observed. And the short-selling of stocks is prohibited. The problem is formulated as a stochastic linear-quadratic (LQ) optimal control problem where the control variables are constrained. Based on the separation principle and stochastic filtering theory, the partial information problem is solved. Efficient strategies and efficient frontier are presented in closed forms via solutions to two extended stochastic Riccati equations. As a comparison, the efficient strategies and efficient frontier are given by the viscosity solution for the Hamilton-Jacobi-Bellman (HJB) equation in the full information case. Some numerical illustrations are also provided.

Expectile bears some interesting properties in comparison to the industry wide expected shortfall in terms of assessment of tail risk. We study the relationship between expectile and expected shortfall using duality results and the link to optimized certainty equivalent. Lower and upper bounds of expectile are derived in terms of expected shortfall as well as a characterization of expectile in terms of expected shortfall. Further, we study the asymptotic behavior of expectile with respect to expected shortfall as the confidence level goes to $1$ in terms of extreme value distributions. We use concentration inequalities to illustrate that the estimation of value at risk requires larger sample size than expected shortfall and expectile for heavy tail distributions when $\alpha$ is close to $1$. Illustrating the formulation of expectile in terms of expected shortfall, we also provide explicit or semi-explicit expressions of expectile and some simulation results for some classical distributions.

In this paper we present results on scalar risk measures in markets with transaction costs. Such risk measures are defined as the minimal capital requirements in the cash asset. First, some results are provided on the dual representation of such risk measures, with particular emphasis given on the space of dual variables as (equivalent) martingale measures and prices consistent with the market model. Then, these dual representations are used to obtain the main results of this paper on time consistency for scalar risk measures in markets with frictions. It is well known from the superhedging risk measure in markets with transaction costs, as in Jouini and Kallal (1995), Roux and Zastawniak (2016), and Loehne and Rudloff (2014), that the usual scalar concept of time consistency is too strong and not satisfied. We will show that a weaker notion of time consistency can be defined, which corresponds to the usual scalar time consistency but under any fixed consistent pricing process. We will prove the equivalence of this weaker notion of time consistency and a certain type of backward recursion with respect to the underlying risk measure with a fixed consistent pricing process. Several examples are given, with special emphasis on the superhedging risk measure.

Mathematical models, calibrated to data, have become ubiquitous to make key decision processes in modern quantitative finance. In this work, we propose a novel framework for data-driven model selection by integrating a classical quantitative setup with a generative modelling approach. Leveraging the properties of the signature, a well-known path-transform from stochastic analysis that recently emerged as leading machine learning technology for learning time-series data, we develop the Sig-SDE model. Sig-SDE provides a new perspective on neural SDEs and can be calibrated to exotic financial products that depend, in a non-linear way, on the whole trajectory of asset prices. Furthermore, we our approach enables to consistently calibrate under the pricing measure $\mathbb Q$ and real-world measure $\mathbb P$. Finally, we demonstrate the ability of Sig-SDE to simulate future possible market scenarios needed for computing risk profiles or hedging strategies. Importantly, this new model is underpinned by rigorous mathematical analysis, that under appropriate conditions provides theoretical guarantees for convergence of the presented algorithms.

Policymakers in developing countries increasingly see science, technology, and innovation (STI) as an avenue for meeting sustainable development goals (SDGs), with STI-based startups as a key part of these efforts. Market failures call for government interventions in supporting STI for SDGs and publicly-funded incubators can potentially fulfil this role. Using the specific case of India, we examine how publicly-funded incubators could contribute to strengthening STI-based entrepreneurship. India's STI policy and its links to societal goals span multiple decades -- but since 2015 these goals became formally organized around the SDGs. We examine why STI-based incubators were created under different policy priorities before 2015, the role of public agencies in implementing these policies, and how some incubators were particularly effective in addressing the societal challenges that can now be mapped to SDGs. We find that effective incubation for supporting STI-based entrepreneurship to meet societal goals extended beyond traditional incubation activities. For STI-based incubators to be effective, policymakers must strengthen the 'incubation system'. This involves incorporating targeted SDGs in specific incubator goals, promoting coordination between existing incubator programs, developing a performance monitoring system, and finally, extending extensive capacity building at multiple levels including for incubator managers and for broader STI in the country.

In this work, we attempt to provide a comprehensive granular account of the pace of technological change. More specifically, we survey estimated yearly performance improvement rates for nearly all definable technologies for the first time. We do this by creating a correspondence of all patents within the US patent system to a set of technology domains. A technology domain is a body of patented inventions achieving the same technological function using the same knowledge and scientific principles. We obtain a set of 1757 domains using an extension of the previously defined classification overlap method (COM). These domains contain 97.14% of all patents within the entire US patent system. From the identified patent sets, we calculated the average centrality of the patents in each domain to estimate their improvement rates, following a methodology tested in prior work. The estimated improvement rates vary from a low of 1.9% per year for the Mechanical Skin treatment - Hair Removal and wrinkles domain to a high of 228.8% per year for the Network management - client-server applications domain. We developed a one-line descriptor identifying the technological function achieved and the underlying knowledge base for the largest 50, fastest 20 as well as slowest 20 of these domains, which cover more than forty percent of the patent system. In general, the rates of improvement were not a strong function of the patent set size and the fastest improving domains are predominantly software-based. We make available an online system that allows for automated searching for domains and improvement rates corresponding to any technology of interest to researchers, strategists and policy formulators.

A set of data with positive values follows a Pareto distribution if the log-log plot of value versus rank is approximately a straight line. A Pareto distribution satisfies Zipf's law if the log-log plot has a slope of -1. Since many types of ranked data follow Zipf's law, it is considered a form of universality. We propose a mathematical explanation for this phenomenon based on Atlas models and first-order models, systems of positive continuous semimartingales with parameters that depend only on rank. We show that the stable distribution of an Atlas model will follow Zipf's law if and only if two natural conditions, conservation and completeness, are satisfied. Since Atlas models and first-order models can be constructed to approximate systems of time-dependent rank-based data, our results can explain the universality of Zipf's law for such systems. However, ranked data generated by other means may follow non-Zipfian Pareto distributions. Hence, our results explain why Zipf's law holds for word frequency, firm size, household wealth, and city size, while it does not hold for earthquake magnitude, cumulative book sales, the intensity of solar flares, and the intensity of wars, all of which follow non-Zipfian Pareto distributions.