Author(s)

Marina Di Giacinto^1,2

¹Dipartimento di Economia e Giurisprudenza, Università degli studi di Cassino e del Lazio Meridionale, Cassino (FR), Italy.
²Dipartimento di Discipline Matematiche, Finanza Matematica ed Econometria, Università Cattolica del Sacro Cuore, Milano, Italy.

While numerical approaches to solve financial and actuarial stochastic optimization problems are usually based on dynamic programming, we explore an approach through a stochastic maximum principle formulation followed by the use of least squares regression to determine the optimal control policy. We show that this methodology can be applied to a number of realistic financial and actuarial problems of increasing complexity to highlight potential strengths and applications of this approach. We cast a direct connection between this approach and the stochastic duality approach to stochastic optimization. In particular, we discuss the potential improvements which can derive from this reformulation in terms of numerical precision and in order to provide bounds to control the simulation errors. The critical numerical issue is shown to be the numerical computation of conditional expectations which is performed applying the approach of Longstaff and Schwartz [1].

Least Square Method, Stochastic Optimal Control, Stochastic Maximum Principle, Backward Stochastic Differential Equation, Portfolio Choice

Giacinto, M. (2018) Numerical Methods in Financial and Actuarial Applications: A Stochastic Maximum Principle Approach. Journal of Mathematical Finance, 8, 283-301. doi: 10.4236/jmf.2018.82019.