2023 Australasian Actuarial Education and Research Symposium

Ning Wang

Macquarie University

Investment-consumption optimization with transaction cost and learning about return predictability

This is joint work with Tak Kuen Siu

In this paper, we investigate an investment-consumption optimization problem. The expected return of the risky asset is predictable with an observable and an unobservable factor, and the decision-maker has to learn about the latter one. Both factors are supposed to follow a mean-reverting process. Also, we relax the assumption of perfect liquidity of the risky asset by considering its proportional transaction cost. In such way, a form of friction posing liquidity risk to the investor is examined. Dynamic programming principle coupled with Hamilton–Jacobi–Bellman equation is adopted to solve this stochastic optimal control problem. Applying an asymptotic method with small transaction costs being taken as a perturbation parameter, we determine the frictional value function by solving the first and second corrector equations. In the meantime, Monte Carlo simulation based approximation algorithm is adopted to solve the second corrector equation. Finally, some numerical examples and their economic interpretations are discussed.