Abstract
We consider an optimal selection problem for bid and ask quotes subject to a value-at-Risk (VaR) constraint when arrivals of the buy and sell orders are governed by a Poisson process. The problem is formulated as a constrained utility maximization problem over a finite time horizon. Using a diffusion approximation to Poisson arrivals of market orders, the dynamic programming principle can be applied here. We propose an efficient procedure to solve this constrained utility maximization problem based on a successive approximation algorithm. Numerical examples with and without the VaR constraint are used to illustrate the effect of the risk constraint on the dealer's choices. We also conduct numerical experiments to analyze the impacts of the risk constraint on dealer's terminal profit.
Original language | English |
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Title of host publication | Proceedings of the 2012 5th International Joint Conference on Computational Sciences and Optimization, CSO 2012 |
Pages | 266-270 |
Number of pages | 5 |
DOIs | |
Publication status | Published - 31 Oct 2012 |
Event | 2012 5th International Joint Conference on Computational Sciences and Optimization, CSO 2012 - Harbin, Heilongjiang, China Duration: 23 Jun 2012 → 26 Jun 2012 |
Conference
Conference | 2012 5th International Joint Conference on Computational Sciences and Optimization, CSO 2012 |
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Country/Territory | China |
City | Harbin, Heilongjiang |
Period | 23/06/12 → 26/06/12 |
Keywords
- Diffusion Approximation
- High-frequency trading
- HJB equations
- Limit order book
- VaR
ASJC Scopus subject areas
- Computational Mathematics
- Theoretical Computer Science