Pandemic Portfolio Choice

Abstract

COVID-19 has taught us that a pandemic can significantly increase biometric risk and at the same time trigger crashes of the stock market. Taking these potential co-movements of financial and non-financial risks into account, we study the portfolio problem of an agent who is aware that a future pandemic can affect her health and personal finances. To model the financial and non-financial aspects of a pandemic, our framework involves a Markov chain capturing the pandemic state of the society and a state-dependent jump-diffusion model of the stock market. In particular, we allow for pandemic-induced stock market crashes similar to the crash that we witnessed at the beginning of March, 2020. The corresponding stochastic dynamic optimization problem is complex: It is characterized by a system of Hamilton-Jacobi-Bellman equations which are coupled with optimality conditions that are only implicitly given. We prove that the agent's value function and optimal policies are determined by the unique global solution to a system of non-linear ordinary differential equations. From an economic point of view, we show that the optimal portfolio strategy is significantly affected by the mere threat of a potential pandemic.