Risk-Sensitive Asset Management and Cascading Defaults

Published Online:https://doi.org/10.1287/moor.2017.0856

References

  • Aktar Y, Taflin E (2014) A remark on smooth solutions to a stochastic control problem with a power terminal cost function and stochastic volatility. Math. Financial Econom. 8(4):489–509.CrossrefGoogle Scholar
  • Bakshi N, Mohan S (2015) Mitigating disruption cascades in supply networks. Working paper, London Business School, London.Google Scholar
  • Basel Committee on Banking Supervision (2009) Findings on the interaction of market and credit risk. Technical report, Bank for International Settlements, Basel, Switzerland.Google Scholar
  • Bayraktar E, Cohen A (2016) Risk sensitive control of the lifetime ruin problem. Appl. Math. Optim., ePub ahead of print August 4, http://doi.org/10.1007/s00245-016-9372-2.CrossrefGoogle Scholar
  • Bayraktar E, Yao S (2013) A weak dynamic programming principle for zero-sum stochastic differential games with unbounded controls. SIAM J. Control Optim. 51(3):2036–2080.CrossrefGoogle Scholar
  • Bayraktar E, Zhang Y (2015) Minimizing the probability of lifetime ruin under ambiguity aversion. SIAM J. Control Optim. 53(1):58–90.CrossrefGoogle Scholar
  • Bebernes JW, Schmitt K (1977) Invariant sets and the Hukuhara-Kneser property for systems of parabolic partial differential equations. Rocky Mountain J. Math. 7(3):557–567.CrossrefGoogle Scholar
  • Bebernes JW, Schmitt K (1979) On the existence of maximal and minimal solutions for parabolic partial differential equations. Proc. AMS 73(2):211–218.CrossrefGoogle Scholar
  • Becherer D, Schweizer M (2005) Classical solutions to reaction-diffusion systems for hedging problems with interacting Itô and point processes. Ann. Appl. Probab. 15(2):1111–1144.CrossrefGoogle Scholar
  • Bielecki TR, Pliska SR (1999) Risk-sensitive dynamic asset management. Appl. Math. Optim. 39(3):337–360.CrossrefGoogle Scholar
  • Bielecki TR, Pliska SR (2000) Risk sensitive asset management with transaction costs. Finance Stochastics 4(1):1–33.CrossrefGoogle Scholar
  • Bielecki TR, Pliska SR, Sheu SJ (2006) Risk sensitive portfolio management with Cox–Ingersoll–Ross interest rates: The HJB equation. SIAM J. Control Optim. 44(5):1811–1843.CrossrefGoogle Scholar
  • Bienstock D (2011) Optimal control of cascading power grid failures. Proc. 50th IEEE Conf. Decision Control Eur. Control Conf., CDC-ECC ’11 (IEEE, Piscataway, NJ), 2166–2173.CrossrefGoogle Scholar
  • Brennan M, Xia Y (2000) Stochastic interest rates and the bond-stock mix. Euro. Financial Rev. 4(2):197–210.CrossrefGoogle Scholar
  • Campbell J, Taksler G (2003) Equity volatility and corporate bond yields. J. Finance 58(6):2321–2350.CrossrefGoogle Scholar
  • Capponi A, Frei C (2016) Systemic influences on optimal equity-credit investment. Management Sci., ePub ahead of print June 23, http://doi.org/10.1287/mnsc.2016.2460.LinkGoogle Scholar
  • Capponi A, Figueroa-López JE, Pascucci A (2015) Dynamic credit investment in partially observed markets. Finance Stochastics 19(4):891–939.CrossrefGoogle Scholar
  • Carr P, Linetsky V (2006) A jump to default extended CEV model: An application of Bessel processes. Finance Stochastics 10(3):303–330.CrossrefGoogle Scholar
  • Davis M, Lleo S (2015) Risk-Sensitive Investment Management, Advanced Series on Statistical Science and Applied Probability, Vol. 19, 1st ed. (World Scientific, Singapore).Google Scholar
  • Dupuis P, Kushner H (1989) Minimizing escape probabilities: A large deviations approach. SIAM J. Control Optim. 27(2):432–445.CrossrefGoogle Scholar
  • Fleming W (2006) Risk sensitive stochastic control and differential games. Commun. Inform. Syst. 6(3):161–177.CrossrefGoogle Scholar
  • Fleming W, McEneaney W (1995) Risk-sensitive control on an infinite time horizon. SIAM J. Control Optim. 33(6):1881–1915.CrossrefGoogle Scholar
  • Fleming W, Rishel R (1975) Deterministic and Stochastic Optimal Control, Applications of Mathematics, Vol. 1 (Springer, New York).CrossrefGoogle Scholar
  • Fleming W, Soner M (1983) Controlled Markov Processes and Viscosity Solutions, Stochastic Modelling and Applied Probability, Vol. 25, 2nd ed. (Springer, New York).Google Scholar
  • Fouque J, Sircar R, Zariphopoulou T (2015) Portfolio optimization and stochastic volatility asymptotics. Math. Finance, ePub ahead of print September 30, http://doi.org/10.1111/mafi.12109.Google Scholar
  • Hansen L, Sargent T (2005) Robust estimation and control under commitment. J. Econom. Theor. 124(2):258–301.CrossrefGoogle Scholar
  • Hansen L, Sargent T (2007) Recursive robust estimation and control without commitment. J. Econom. Theory 136(1):1–27.CrossrefGoogle Scholar
  • Hansen L, Sargent T, Turmuhambetova G, Williams N (2006) Robust control and model misspecification. J. Econom. Theory 128(1):45–90.CrossrefGoogle Scholar
  • Jiao Y, Kharroubi I, Pham H (2013) Optimal investment under multiple defaults risk: A BSDE-decomposition approach. Ann. Appl. Probab. 23(2):455–491.CrossrefGoogle Scholar
  • Krylov NV (1987) Nonlinear Elliptic and Parabolic Equations of the Second Order, Soviet Series on Mathematics and Its Applications, Vol. 7 (D. Reidel Publishing Co., Dordrecht, Netherlands). [Translated from the Russian by P. L. Buzytsky].CrossrefGoogle Scholar
  • Ladyzhenskaja OA, Solonnikov VA, Uralceva NN (1968) Linear and Quasilinear Equations of Parabolic Type, Translations of Mathematical Monographs, Vol. 23 (American Mathematical Society, Providence, RI). [Translated from the Russian by S. Smith].CrossrefGoogle Scholar
  • Loc NH, Schmitt K (2012) Bernstein–Nagumo conditions and solutions to nonlinear differential inequalities. Nonlinear Anal. TMA 75(12):4664–4671.CrossrefGoogle Scholar
  • Mendoza-Arriaga R, Linetsky V (2016) Multivariate subordination of Markov processes with financial applications. Math. Finance 26(4):699–747.CrossrefGoogle Scholar
  • Nagai H, Peng S (2002) Risk-sensitive dynamic portfolio optimization with partial information on infinite time horizon. Ann. Appl. Probab. 12(1):173–195.CrossrefGoogle Scholar
  • Pham H (2002) Smooth solutions to optimal investment models with stochastic volatilities and portfolio constraints. Appl. Math. Optim. 46(1):55–78.CrossrefGoogle Scholar
  • Sircar R, Zariphopoulou T (2010) Utility valuation of multi-name credit derivatives and application to CDOs. Quant. Finance 10(2):195–208.CrossrefGoogle Scholar
  • Tamura T, Watanabe Y (2011) Risk-sensitive portfolio optimization problems for hidden Markov factors on infinite time horizon. Asymptotic Anal. 75(3):169–209.Google Scholar
  • Whittle P (1990) Risk-Sensitive Optimal Control, Wiley-Interscience Series in Systems and Optimization (John Wiley & Sons, Chichester, UK).Google Scholar
  • Zariphopoulou T (2009) Optimal Asset Allocation in a Stochastic Factor Model-An Overview and Open Problems, Advanced Financial Modeling, Radon Ser. Comput. App. Math., Vol. 8 (Walter de Gruyter, Berlin).Google Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.