Robust investment–reinsurance optimization with multiscale stochastic volatility

Chi Seng Pun and Hoi Ying Wong

Insurance: Mathematics and Economics, 2015, vol. 62, issue C, 245-256

Abstract: 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.

Keywords: Investment and reinsurance; Mixture of power utilities; Hamilton–Jacobi–Bellman–Isaacs equation; Multiscale stochastic volatility; Perturbation methods (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (20)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:62:y:2015:i:c:p:245-256

DOI: 10.1016/j.insmatheco.2015.03.030

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