Restricted Coherent Risk Measures and Actuarial Solvency

We prove a general dual representation form for restricted coherent risk measures, and we apply it to a minimization problem of the required solvency capital for an insurance company.

[1]  B. Roorda,et al.  COHERENT ACCEPTABILITY MEASURES IN MULTIPERIOD MODELS , 2005 .

[2]  B. Øksendal.  Stochastic Differential Equations , 1985 .

[3]  Giacomo Scandolo,et al.  Conditional and dynamic convex risk measures , 2005, Finance Stochastics.

[4]  R. Norberg.  Ruin problems with assets and liabilities of diffusion type , 1999 .

[5]  Christos E. Kountzakis,et al.  Risk measures in ordered normed linear spaces with non-empty cone-interior , 2011 .

[6]  X. Gong,et al.  Connectedness of efficient solution sets for set-valued maps in normed spaces , 1994 .

[7]  Harry H. Panjer,et al.  MEASUREMENT OF RISK, SOLVENCY REQUIREMENTS AND ALLOCATION OF CAPITAL WITHIN FINANCIAL CONGLOMERATES , 2002 .

[8]  G. Pflug.  Some Remarks on the Value-at-Risk and the Conditional Value-at-Risk , 2000 .

[9]  S. Shreve,et al.  Methods of Mathematical Finance , 2010 .

[10]  Ludger Rüschendorf,et al.  On convex risk measures on Lp-spaces , 2009, Math. Methods Oper. Res..

[11]  Christian Hipp,et al.  Asymptotics of ruin probabilities for controlled risk processes in the small claims case , 2004 .

[12]  Qihe Tang,et al.  Solvency capital, risk measures and comonotonicity: a review , 2004 .

[13]  Frank Riedel,et al.  Dynamic Coherent Risk Measures , 2003 .

[14]  W. Schachermayer,et al.  Optimal expected exponential utility of dividend payments in a Brownian risk model , 2007 .

[15]  Demand functions and reflexivity , 2008 .

[16]  G. Jameson.  Ordered Linear Spaces , 1970 .

[17]  Philippe Artzner,et al.  Coherent Measures of Risk , 1999 .

[18]  F. Delbaen.  Coherent Risk Measures on General Probability Spaces , 2002 .

[19]  Damir Filipović,et al.  Monotone and cash-invariant convex functions and hulls , 2007 .

[20]  R. Rockafellar,et al.  Optimization of conditional value-at risk , 2000 .

[21]  V. Barbu,et al.  Convexity and optimization in banach spaces , 1972 .