Choi, Jungmin; Jonsson, Mattias Partial hedging in financial markets with a large agent. (English) Zbl 1178.91194 Appl. Math. Finance 16, No. 3-4, 331-346 (2009). Summary: We investigate the partial hedging problem in financial markets with a large agent. An agent is said to be large if his/her trades influence the equilibrium price. We develop a stochastic differential equation (SDE) with a single large agent parameter to model such a market. We focus on minimizing the expected value of the size of the shortfall in the large agent model. A Bellman-type partial differential equation (PDE) is derived, and the Legendre transform is used to consider the dual shortfall function. An asymptotic analysis leads us to conclude that the shortfall function (expected loss) increases when there is a large agent, which means that one would need more capital to hedge away risk in the market with a large agent. This asymptotic analysis is confirmed by performing Monte Carlo simulations. MSC: 91G20 Derivative securities (option pricing, hedging, etc.) 91B24 Microeconomic theory (price theory and economic markets) 91G80 Financial applications of other theories 91G60 Numerical methods (including Monte Carlo methods) Keywords:partial hedging; large agent; Bellman PDE PDFBibTeX XMLCite \textit{J. Choi} and \textit{M. Jonsson}, Appl. Math. Finance 16, No. 3--4, 331--346 (2009; Zbl 1178.91194) Full Text: DOI References: [1] DOI: 10.1111/j.0960-1627.2004.00179.x · Zbl 1119.91040 · doi:10.1111/j.0960-1627.2004.00179.x [2] DOI: 10.1086/260062 · Zbl 1092.91524 · doi:10.1086/260062 [3] DOI: 10.1007/s00780-007-0050-8 · Zbl 1145.91032 · doi:10.1007/s00780-007-0050-8 [4] Choi J., Partial hedging in financial markets with a large agent (2005) [5] DOI: 10.1137/S036301299834185X · Zbl 1034.91037 · doi:10.1137/S036301299834185X [6] DOI: 10.1023/A:1010054408714 · Zbl 1157.91357 · doi:10.1023/A:1010054408714 [7] DOI: 10.1007/s007800050071 · Zbl 0982.91030 · doi:10.1007/s007800050071 [8] DOI: 10.1214/aoap/1034968136 · Zbl 0856.90011 · doi:10.1214/aoap/1034968136 [9] DOI: 10.1007/s00186-006-0083-3 · Zbl 1132.90375 · doi:10.1007/s00186-006-0083-3 [10] DOI: 10.1007/s007800050062 · Zbl 0977.91019 · doi:10.1007/s007800050062 [11] DOI: 10.1007/s007800050008 · Zbl 0956.60074 · doi:10.1007/s007800050008 [12] DOI: 10.1007/s007800050035 · Zbl 0894.90017 · doi:10.1007/s007800050035 [13] DOI: 10.1111/1467-9965.00036 · Zbl 1020.91023 · doi:10.1111/1467-9965.00036 [14] DOI: 10.1016/0022-0531(79)90043-7 · Zbl 0431.90019 · doi:10.1016/0022-0531(79)90043-7 [15] DOI: 10.1016/0304-4149(81)90026-0 · Zbl 0482.60097 · doi:10.1016/0304-4149(81)90026-0 [16] DOI: 10.1080/1350486022000025471 · Zbl 1042.91044 · doi:10.1080/1350486022000025471 [17] Jonsson M., Modern Methods in Scientific Computing and Applications pp 255– (2002) · doi:10.1007/978-94-010-0510-4_7 [18] DOI: 10.1111/j.1467-9965.2002.tb00130.x · Zbl 1049.91073 · doi:10.1111/j.1467-9965.2002.tb00130.x [19] DOI: 10.1137/S0363012903423168 · Zbl 1101.91041 · doi:10.1137/S0363012903423168 [20] Rockefellar R. T., Convex Analysis (1970) · Zbl 0932.90001 · doi:10.1515/9781400873173 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.