L\'{e}vy Process, Proportional Transaction Costs and Foreign Exchange

  •  Obonye Doctor    
  •  Elias R. Offen    
  •  Edward Lungu    


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 $c\geq0$, $p<1$, $p\neq0$.

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