Finite-horizon optimal investment with transaction costs: construction of the optimal strategies

Abstract

We revisit the problem of maximising expected utility of terminal wealth in a Black-Scholes market with proportional transaction costs. While it is known that the value function of this problem is the unique viscosity solution of the HJB equation and that the HJB equation admits a classical solution on a reduced state space, it has been an open problem to verify that these two coincide. We establish this result by devising a verification procedure based on superharmonic functions. In the process, we construct optimal strategies and provide a detailed analysis of the regularity of the value function.

Optimal Investment Strategy for DC Pension Plan with Deposit Loan Spread under the CEV Model

“…Bian et al [15] and Chen et al [16] investigated the DC pension fund investment problem under a Markovian regime-switching market consisting of one risk-free asset and multiple risky assets. Optimal investment with transaction cost over an infinite horizon was developed by Blake and Sass [17]. The dual control technique was employed to investigate the investment problem constrained by short selling in [18].…”

The optimal investment strategy of a DC pension plan under deposit loan spread and the O-U process

“…Guambe et al (2019) further stated a investment problem, which consists of inflation and mortality risks. Optimal investment with transaction cost over an infinite horizon was developed by Blake and Sass (2002). Based on previous work, Mudzimbabwe (2019a) investigated a unsophisticated numerical solution method.…”