On investment and minimization of shortfall risk for a diffusion model with jumps and two interest rates via market completion

Authors:
Selly Kane and Alexander Melnikov

Translated by:
The authors

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **78** (2008).

Journal:
Theor. Probability and Math. Statist. **78** (2009), 75-82

MSC (2000):
Primary 60H30, 62P05, 91B28; Secondary 60J75, 60G44, 91B30

DOI:
https://doi.org/10.1090/S0094-9000-09-00763-7

Published electronically:
August 4, 2009

MathSciNet review:
2446850

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This paper deals with the problems of investment and shortfall risk minimization in the framework of a two-factor diffusion model with jumps and with different credit and deposit rates. The optimal strategies are derived by means of auxiliary completions of the initial market.

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Additional Information

**Selly Kane**

Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, T6G2G1 Canada

Email:
skane@ualberta.ca

**Alexander Melnikov**

Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, T6G2G1 Canada

Email:
melnikov@ualberta.ca

DOI:
https://doi.org/10.1090/S0094-9000-09-00763-7

Keywords:
Constrained market,
completion,
hedging and pricing,
diffusion with jumps,
different interest rates

Received by editor(s):
January 9, 2007

Published electronically:
August 4, 2009

Additional Notes:
The paper was supported by the discovery grant NSERC #261855

Article copyright:
© Copyright 2009
American Mathematical Society