Constrained expected utility maximization: applications in quantitative finance, risk management, life and pension insurance

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Expected utility maximization has found many interesting applications in asset pricing, optimal portfolio theory, financial, and actuarial risk management. In real situations, the economic agent has to follow regulatory restrictions that eventually induce significant impacts on her optimal investment decision. My research program focuses on new developments of risk management and optimal portfolio choice models in general settings that give new flexibilities and theoretical insights to solve remaining challenges in finance and actuarial science. My research program consists of three long-term objectives. My first objective is to build tractably computational frameworks of risk management. Examples include the case where the optimizing economic agent aims to control the upper bound of the total expected loss defined as the weighted sum of the individual expected losses. I will extend results to settings with intermediate regulations imposed on prefixed intermediate days of the investment time horizon or with multiple investors. It is then interesting to explore regulatory impacts on the individual investment behavior in a Nash equilibrium. My second objective, motivated by the presence of mortality risk and the non-concave payoff structure of participating insurance contracts, concentrates on a non-concave expected utility problem under a random time horizon with risk constraints. I will characterize and construct an algorithm to numerically determine the optimal strategy based on the independence assumption of the death time and the financial market. The results can find various applications in contract design and risk management of equity-linked life insurance contracts. As market impact and ambiguity play a critical role in optimal portfolio choice, my third objective is to study the optimal consumption and investment problem in a financial market where the trading influences the future prices, and price curves are non-linear in volume, capturing endogenous phenomena as non-linearity in liquidation and market contractions due to illiquidity. In such a non-linear endogenous permanent market impact setting, it is possible to characterize optimality in terms of forward-backward stochastic differential equations (FBSDEs). I plan to extend the model to general jump models with time-consistent ambiguity averse preferences and possibly non-convex trading constraints. I will investigate the optimal solution via FBSDEs with jumps and then explore various applications to indifference pricing of insurance contracts and untradable derivatives.