Synowiec, D: Investor Problem

Optimal portfolio selection problems have been investigated since the late 1960‘s. Most of them are concerned with investment in a savings account on a constant rate and a finite number of stocks. Then the explicit solution is given. Over the last few years, a problem of an investment in the bond market, with an interest rate changing in time but without possibility of consumption, has been considered. In this book, it is considered an investor problem with an interest rate given by a stochastic differential equation and with possibility of consumption as well as investing money both in savings account and in zero-coupon bonds. There are given formulae for both optimal portfolio and optimal consumption strategy. On the other hand, an investor problem in discrete time case with forward rate given by Markov chain is analyzed. Theoretical results are illustrated with interesting examples. The book should be useful to all interested in applications of stochastic control theory, or anyone else whose area of interest is financial mathematics.