International Journal of Stochastic Analysis
Volume 2011 (2011), Article ID 942478, 19 pages
Research Article

Optimal Harvesting When the Exchange Rate Is a Semimartingale

Department of Mathematics, Faculty of Science, University of Botswana, Private Bag UB 0022, Gaborone, Botswana

Received 8 August 2011; Revised 31 October 2011; Accepted 1 November 2011

Academic Editor: Onesimo Hernandez Lerma

Copyright © 2011 E. R. Offen and E. M. Lungu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider harvesting in the Black-Scholes Quanto Market when the exchange rate is being modeled by the process 𝐸 𝑡 = 𝐸 0 e x p { 𝑋 𝑡 } , where 𝑋 𝑡 is a semimartingale, and we ask the following question: What harvesting strategy 𝛾 and the value function Φ maximize the expected total income of an investment? We formulate a singular stochastic control problem and give sufficient conditions for the existence of an optimal strategy. We found that, if the value function is not too sensitive to changes in the prices of the investments, the problem reduces to that of Lungu and Øksendal. However, the general solution of this problem still remains elusive.