A maximum principle for relaxed stochastic control of linear SDE's with application to bond portfolio optimization

TL;DR

This paper develops a maximum principle for relaxed stochastic control of linear SDEs with unbounded coefficients, applying it to optimize bond portfolios with measure-valued weights in a market with a continuum of bonds.

Contribution

It introduces a relaxed maximum principle for linear SDEs with unbounded coefficients and demonstrates its application to bond portfolio optimization.

Findings

Existence of an optimal relaxed control.

Necessary conditions for optimality via a relaxed maximum principle.

Application to continuum of bonds in financial markets.

Abstract

We study relaxed stochastic control problems where the state equation is a one dimensional linear stochastic differential equation with random and unbounded coefficients. The two main results are existence of an optimal relaxed control and necessary conditions for optimality in the form of a relaxed maximum principle. The main motivation is an optimal bond portfolio problem in a market where there exists a continuum of bonds and the portfolio weights are modeled as measure-valued processes on the set of times to maturity.