Abstract
We analyse optimal portfolio selection problem of maximizing the utility of an agent who invests in a stock and money market account in the presence of proportional transaction cost $\lambda>0$ and foreign exchange rate. The stock price follows a (generalized) Geometric It\^{o}-L\'{e}vy process. The utility function is $U(c)={c^{p}}/{p}$ for all $c\geq0$, $p<1$, $p\neq0$.
Highlights
The study of dynamic portfolio choice has a long history, tracking back to Merton (1971)
We analyse optimal portfolio selection problem of maximizing the utility of an agent who invests in a stock and money market account in the presence of proportional transaction cost λ > 0 and foreign exchange rate
The introduction of the jumps to the Merton model where the dynamics of stock price are modelled by a Levy process has attracted a lot of researchers; Øksendal and Sulem (2004, 2005, 2014), Tankov (2005) and many more
Summary
The study of dynamic portfolio choice has a long history, tracking back to Merton (1971). Our work is motivated by Øksendal and Sulem (2014) on their quick introduction to some important tools in the modern research within mathematical finance, with emphasis on applications to portfolio optimization and risk minimization, Liu (2004) by successfully analyzing and deriving the optimal transaction policy in an explicit form when n ≥ 1 risky assets are correlated and subject to fixed transaction costs in an infinite horizon, Janecek and Shreve (2004) and Bichuch (2011) by considering the cases where an agent invests in a stock and a money market account with the hope of maximizing his/her wealth in an infinite time horizon and at the final time T , respectively, in the presence of the proportional transaction costs.
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