Robust Optimal Investment Research Articles

Robust optimal investment and reinsurance of an insurer under variance premium principle and default risk

This paper considers a robust optimal investment and reinsurance problem under model ambiguity and default risk for an insurer, who can trade in a saving account, a stock and a defaultable bond and aims to maximize the minimal expected CARA utility. The surplus process of the insurer is assumed to follow the Cramér–Lundberg model. In particular, both the insurance and reinsurance premium are assumed to be calculated via the variance premium principle. By using the dynamic programming approach, we study the pre-default case and post-default case respectively, then closed-form expressions for the optimal strategies and the corresponding value function are derived. Finally, numerical examples are given to illustrate our main results, and we discuss relevant economic insights obtained from these results.

Robust investment–reinsurance optimization with multiscale stochastic volatility

This paper investigates the investment and reinsurance problem in the presence of stochastic volatility for an ambiguity-averse insurer (AAI) with a general concave utility function. The AAI concerns about model uncertainty and seeks for an optimal robust decision. We consider a Brownian motion with drift for the surplus of the AAI who invests in a risky asset following a multiscale stochastic volatility (SV) model. We formulate the robust optimal investment and reinsurance problem for a general class of utility functions under a general SV model. Applying perturbation techniques to the Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation associated with our problem, we derive an investment–reinsurance strategy that well approximates the optimal strategy of the robust optimization problem under a multiscale SV model. We also provide a practical strategy that requires no tracking of volatility factors. Numerical study is conducted to demonstrate the practical use of theoretical results and to draw economic interpretations from the robust decision rules.

Robust worst-case optimal investment

Based on a robustness concept adapted from mathematical statistics, we investigate robust optimal investment strategies for worst-case crash scenarios when the maximum crash height is not known a priori. We specify an efficiency criterion in terms of the certainty equivalents of optimal terminal wealth and explicitly solve the investor's portfolio problem for CRRA risk preferences. We also study the behavior of the minimax crash height and the efficiency of the associated strategies in the limiting case of infinitely many crashes.

Robust optimal control for an insurer with reinsurance and investment under Heston’s stochastic volatility model

This paper considers a robust optimal reinsurance and investment problem under Heston’s Stochastic Volatility (SV) model for an Ambiguity-Averse Insurer (AAI), who worries about model misspecification and aims to find robust optimal strategies. The surplus process of the insurer is assumed to follow a Brownian motion with drift. The financial market consists of one risk-free asset and one risky asset whose price process satisfies Heston’s SV model. By adopting the stochastic dynamic programming approach, closed-form expressions for the optimal strategies and the corresponding value functions are derived. Furthermore, a verification result and some technical conditions for a well-defined value function are provided. Finally, some of the model’s economic implications are analyzed by using numerical examples and simulations. We find that ignoring model uncertainty leads to significant utility loss for the AAI. Moreover we propose an alternative model and associated investment strategy which can be considered more adequate under certain finance interpretations, and which leads to significant improvements in our numerical example.

Robust Worst-Case Optimal Investment

Based on a robustness concept adapted from mathematical statistics, we investigate robust optimal investment strategies for worst-case crash scenarios when the maximum crash height is not known a priori. We specify an efficiency criterion in terms of the certainty equivalents of optimal terminal wealth and explicitly solve the investor’s portfolio problem for CRRA risk preferences. We also study the behavior of the minimax crash height and the efficiency of the associated strategies in the limiting case of infinitely many crashes.