Robust Investment-Reinsurance Optimization with Multiscale Stochastic Volatility

37 Pages Posted: 23 Jun 2020

See all articles by Chi Seng Pun

Chi Seng Pun

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences

Hoi Ying Wong

The Chinese University of Hong Kong (CUHK) - Department of Statistics

Date Written: April 11, 2015

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

Suggested Citation

Pun, Chi Seng and Wong, Hoi Ying, Robust Investment-Reinsurance Optimization with Multiscale Stochastic Volatility (April 11, 2015). Insurance: Mathematics and Economics, 62, 245-256, Available at SSRN: https://ssrn.com/abstract=3613759

Chi Seng Pun (Contact Author)

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences ( email )

SPMS-MAS-05-22
21 Nanyang Link
Singapore, 637371
Singapore
(+65) 6513 7468 (Phone)

HOME PAGE: http://personal.ntu.edu.sg/cspun/

Hoi Ying Wong

The Chinese University of Hong Kong (CUHK) - Department of Statistics ( email )

Shatin, N.T.
Hong Kong

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