On the spanning property of risk bonds priced by equilibrium

Mathematics of Operations Research

Volumn 32, Issue 4, 2007, Pages 784-807

  Horst, Ulrich ^a   Müller, Matthias ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Backward stochastic differential equations; Climate risk; Partial equilibrium; Pricing in illiquid financial markets

Indexed keywords

BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS; CLIMATE RISK; PARTIAL EQUILIBRIUM; PRICING IN ILLIQUID FINANCIAL MARKETS;

DIFFERENTIAL EQUATIONS; MARKETING; NUMERICAL ANALYSIS; RISK ANALYSIS; STOCHASTIC CONTROL SYSTEMS;

FINANCE;

EID: 38549109106     PISSN: 0364765X     EISSN: 15265471     Source Type: Journal    
DOI: 10.1287/moor.1070.0270     Document Type: Article

References (40)

1. Barrieu, P., N. El Karoui. 2002. Optimal design of derivatives in illiquid framework. Quant. Finance 2 1-8.
2. Barrieu, P., N. El Karoui. 2005. Inf-convolution of risk measures and optimal risk transfer. Finance and Stochastics 9 269-298.
3. Becherer, D. 2004. Utility indifference hedging and valuation via reaction diffusion systems. Proc. Roy. Soc., Ser. A 460 27-51.
4. Becherer, D. 2006. Bounded solutions to backward SDE's with jumps for utility optimization and indifference hedging. Ann. Appl. Probab. 16(4) 2027-2054.
5. Bouchard, B., N. Touzi. 2004. Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations. Stochastic Processes and Their Appl. 111(2) 175-206.
6. Briant, P., Y. Hu. 2006. BSDE with quadratic growth and unbounded terminal value. Probab. Theory Related Fields 136(4) 604-618.
7. Chaumont, S., P. Imkeller, M. Müller. 2004. Equilibrium trading of climate and weather risk and numerical simulation in a Markovian framework. Stochastic Environ. Res. Risk Assessment 20 184-205.
8. Chaumont, S., U. Horst, P. Imkeller, M. Müller. 2005. A simple model of trading climate risk. Vierteljahrshefte zur Wirtschaftsforschung 74 175-195.
9. Cheridito, P., M. Soner, N. Touzi, N. Victoir. 2005. Second order backward stochastic differential equations and fully non-linear parabolic PDEs. Comm. Pure Appl. Math. 60(7) 1081-1110.
10. Davis, M. 1998. Option pricing in incomplete markets. M. A. H. Dempster, S. R. Pliska, eds. Mathematics of Derivative Securities. Cambridge University Press, Cambridge, UK.
11. Davis, M. 2000. Optimal hedging with basic risk. Working paper, Technical University, Vienna, Austria.
12. Davis, M. 2001. Pricing weather derivatives by marginal value. Quant. Finance 1 305-308.
13. Duffie, D., H. Richardson. 1991. Mean-variance hegding in continuous time. Ann. Appl. Probab. 11-15.
14. El Karoui, N., S. Quenez. 1995. Dynamic programming and pricing in incomplete markets. SIAM J. Control Optim. 33 29-66.
15. El Karoui, N., N. Peng, S. Quenez. 1997. Backward stochastic differential equations in finance. Math. Finance 7 1-71.
16. Föllmer, H., P. Leukert. 1999. Quantile hedging. Finance and Stochastics 3 251-273.
17. Föllmer, H., P. Leukert. 2000. Efficient hedges: Cost versus shortfall risk. Finance and Stochastics 4 117-146.
18. Föllmer, H., D. Sondermann. 1986. Hedging of nonredundant contingent claims. W Hildenbrand, A. Mas-Colell, eds. Contributions to Mathematical Economics, in Honor of G. Debreu, Elsevier Science Publ., North-Holland, 205-223.
19. Gaol, J. L., D. Manurung. 2000. El Nino Southern Oscillation impact on sea surface temperature derived from satellite and its relationships on tuna fishing ground in the South Java seawaters. AARS.
20. Henderson, V, D. Hobson. 2007. Utility indifference pricing: An overview. R. Carmona, ed. Volume on Indifference Pricing. Princeton University Press. Princeton, NJ. To appear.
21. Hu, Y. P., P. Imkeller, M. Müller. 2005. Market completion and partial equilibrium. Internat. J. Theoret. Appl. Finance 8(4) 483-508.
22. Jakobsen, E. R., K. H. Karlsen. 2002. Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate parabolic equations. J. Differential Equations 183 497-525.
23. Karatzas, I., J. P. Lehoczky, S. E. Shreve. 1990. Existence and uniqueness of multi-agent equilibrium in a stochastic, dynamic consumption/investment model. Math. Oper. Res. 15 80-128.
24. Kazamaki, N. 1994. Continuous exponential martingales and BMO. Lecture Notes in Mathematics, Vol. 1579. Springer, Berlin, Germany.
25. Kobylanski, M. 2000. Backward stochastic differential equations and partial differential equations with quadratic growth. Ann. Probab. 28 558-602.
26. Ladyzenskaja, O. A., V A. Solonnikov, N. N. Ural'ceva. 1968. Linear and Quasi-Linear Equations of Parabolic Type. American Mathematical Society, Providence, RI.
27. Lazrak, A. 2004. Generalized stochastic differential utility and preference for information. Ann. Appl. Probab. 14(4) 2149-2175.
28. Mania, M., M. Schweizer. 2005. Dynamic exponential utility indifference valuation. Ann. Appl. Probab. 15(3) 2113-2143.
29. Moeller, T. 2003. Indifference pricing of insurance contracts in a product space model. Finance and Stochastics 7 197-217.
30. Müller, M. 2005. Market completion and robust utility maximization. Ph.D. dissertation, Humboldt University, Berlin, Germany.
31. Musiela, M., T. Zariphopoulou. 2004a. An example of indifference prices under exponential preferences. Finance and Stochastics 8 229-239.
32. Musiela, M., T. Zariphopoulou. 2004b. A valuation algorithm for indifference prices in incomplete markets. Finance and Stochastics 8 399-4-14.
33. Nualart, D. 1995. The Malliavin Calculus and Related Topics. Springer, Berlin, Germany.
34. Pardoux, E., S. G. Peng. 1990. Adapted solution of a backward stochastic differential equation. Systems and Control Lett. 14 55-61.
35. Revuz, D., M. Yor. 1994. Continuous Martingales and Brownian Motion. Springer, Berlin, Germany.
36. Schweizer, M. 1992. Mean-variance hedging for general claims. Ann. Appl. Probab. 2 171-176.
37. Schweizer, M. 2001. From actuarial to financial valuation principles. Insurance: Math. Econom. 28 31-47.
38. Swiss Re. 1998. Sigma No. 3 Technical report, Zurich, Switzerland.
39. Taylor, M. E. 1996. Partial Differential Equations III, Applied Mathematical Sciences, Vol. 117. Springer-Verlag, Berlin, Germany.
40. World Bank, The. 2005. Managing agricultural production risk. Report 32727-GLB, Washington, D.C.