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# Dividing gains between a client and her agent

## Author

Listed:
• Jianming Xia

() (Institute of Applied Mathematics, Academy of Mathematics and System Sciences Chinese Academy of Sciences, P.O. Box 2734, Beijing 100080, China Manuscript)

## Abstract

A client(she) contracts with an agent(him), who has limited liability, as follows: she lends him one dollar at time 0 and he uses the money to trade in a security market. As return, he promises to give her a fixed amount $e^{r_0T}$ at the final time T; in addition, if the real return rate of the strategy is larger than $r_0$, she can also get a fixed proportion $(1-\alpha)$ of the "excess profit" and he will take the rest. Assume that the market is complete and the agent aims to maximize the risk-neutral value of his profit subject to some expected shortfall constraint. The reasonable benchmark return rate $r_0$ and the proportion $\alpha$ are explicitly worked out.

## Suggested Citation

• Jianming Xia, 2003. "Dividing gains between a client and her agent," Finance and Stochastics, Springer, vol. 7(2), pages 219-230.
• Handle: RePEc:spr:finsto:v:7:y:2003:i:2:p:219-230
Note: received: April 2001; final version received: June 2002
as

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## References listed on IDEAS

as
1. Küchler, Uwe & Tappe, Stefan, 2008. "Bilateral gamma distributions and processes in financial mathematics," Stochastic Processes and their Applications, Elsevier, vol. 118(2), pages 261-283, February.
2. Vicky Henderson & Rafal Wojakowski, 2001. "On the Equivalence of Floating and Fixed-Strike Asian Options," OFRC Working Papers Series 2001mf08, Oxford Financial Research Centre.
3. José Fajardo & Ernesto Mordecki, 2014. "Skewness premium with Lévy processes," Quantitative Finance, Taylor & Francis Journals, vol. 14(9), pages 1619-1626, September.
4. Peter Carr & Katrina Ellis & Vishal Gupta, 1998. "Static Hedging of Exotic Options," Journal of Finance, American Finance Association, vol. 53(3), pages 1165-1190, June.
Full references (including those not matched with items on IDEAS)

## More about this item

### Keywords

Agency; investment; Neyman-Pearson lemma; complete market;

### JEL classification:

• D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
• G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
• G20 - Financial Economics - - Financial Institutions and Services - - - General

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