Wang, Wei; Jin, Zhuo; Qian, Linyi; Su, Xiaonan Local risk minimization for vulnerable European contingent claims on nontradable assets under regime switching models. (English) Zbl 1344.49031 Stochastic Anal. Appl. 34, No. 4, 662-678 (2016). Summary: This article focuses on an optimal hedging problem of the vulnerable European contingent claims. The underlying asset of the vulnerable European contingent claims is assumed to be nontradable. The interest rate, the appreciation rate and the volatility of risky assets are modulated by a finite-state continuous-time Markov chain. By using the local risk minimization method, we obtain an explicit closed-form solution for the optimal hedging strategies of the vulnerable European contingent claims. Further, we consider a problem of hedging for a vulnerable European call option. Optimal hedging strategies are obtained. Finally, a numerical example for the optimal hedging strategies of the vulnerable European call option in a two-regime case is provided to illustrate the sensitivities of the hedging strategies. Cited in 3 Documents MSC: 49J55 Existence of optimal solutions to problems involving randomness 60H30 Applications of stochastic analysis (to PDEs, etc.) 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60J28 Applications of continuous-time Markov processes on discrete state spaces 60J27 Continuous-time Markov processes on discrete state spaces 93E20 Optimal stochastic control 91B30 Risk theory, insurance (MSC2010) 91G80 Financial applications of other theories 65C05 Monte Carlo methods Keywords:European contingent claims; default risk; local risk minimization; continuous-time Markov chain; regime switching; non-tradable assets; Monte Carlo simulation PDF BibTeX XML Cite \textit{W. Wang} et al., Stochastic Anal. Appl. 34, No. 4, 662--678 (2016; Zbl 1344.49031) Full Text: DOI References: [1] DOI: 10.1111/j.1467-9965.2009.00384.x · Zbl 1185.91092 · doi:10.1111/j.1467-9965.2009.00384.x [2] DOI: 10.1016/j.jedc.2006.06.005 · Zbl 1163.91388 · doi:10.1016/j.jedc.2006.06.005 [3] DOI: 10.1007/978-3-540-30788-4_8 · doi:10.1007/978-3-540-30788-4_8 [4] DOI: 10.1080/07362990701857194 · Zbl 1133.91415 · doi:10.1080/07362990701857194 [5] DOI: 10.1007/s10436-005-0013-z · Zbl 1233.91270 · doi:10.1007/s10436-005-0013-z [6] Föllmer H., Computational Management Science, Hildenbrand, W., and M.-C. A. Eds pp 205– (1986) [7] DOI: 10.1137/S0363012996299302 · Zbl 0891.93081 · doi:10.1137/S0363012996299302 [8] DOI: 10.1002/asmb.2028 · doi:10.1002/asmb.2028 [9] DOI: 10.2307/2329239 · doi:10.2307/2329239 [10] DOI: 10.1111/0022-1082.00389 · doi:10.1111/0022-1082.00389 [11] Lee K., Communications on Stochastic Analysis 2 (1) pp 125– (2008) [12] DOI: 10.1080/14697680601043191 · Zbl 1151.91523 · doi:10.1080/14697680601043191 [13] DOI: 10.2143/AST.28.1.519077 · Zbl 1168.91417 · doi:10.2143/AST.28.1.519077 [14] DOI: 10.1088/1469-7688/4/3/001 · doi:10.1088/1469-7688/4/3/001 [15] DOI: 10.1080/13504861003650883 · Zbl 1202.91323 · doi:10.1080/13504861003650883 [16] DOI: 10.1016/j.spa.2014.04.001 · Zbl 1348.60067 · doi:10.1016/j.spa.2014.04.001 [17] DOI: 10.1016/j.insmatheco.2011.10.001 · Zbl 1235.91104 · doi:10.1016/j.insmatheco.2011.10.001 [18] Schweizer M., Hedging of options in a general semimartingale model (1988) [19] DOI: 10.1017/CBO9780511569708.016 · doi:10.1017/CBO9780511569708.016 [20] DOI: 10.1016/j.econmod.2012.09.041 · doi:10.1016/j.econmod.2012.09.041 [21] DOI: 10.1016/j.insmatheco.2008.05.002 · Zbl 1152.91550 · doi:10.1016/j.insmatheco.2008.05.002 [22] DOI: 10.1016/j.insmatheco.2008.03.001 · Zbl 1141.91549 · doi:10.1016/j.insmatheco.2008.03.001 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.