2013/01/15 by Dilip B. Madan, Madan, Dilip, Martijn Pistorius +3
Decision Sciences · Economics, Econometrics and Finance · Engineering · #60Fxx #60H10 #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Reservoir Engineering and Simulation Methods #Risk Management (q-fin.RM) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1301.3531
openalex publication_date 2013/01/15 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
In this paper we propose the notion of continuous-time dynamic spectral\nrisk-measure (DSR). Adopting a Poisson random measure setting, we define this\nclass of dynamic coherent risk-measures in terms of certain backward stochastic\ndifferential equations. By establishing a functional limit theorem, we show\nthat DSRs may be considered to be (strongly) time-consistent continuous-time\nextensions of iterated spectral risk-measures, which are obtained by iterating\na given spectral risk-measure (such as Expected Shortfall) along a given\ntime-grid. Specifically, we demonstrate that any DSR arises in the limit of a\nsequence of such iterated spectral risk-measures driven by lattice-random\nwalks, under suitable scaling and vanishing time- and spatial-mesh sizes. To\nillustrate its use in financial optimisation problems, we analyse a dynamic\nportfolio optimisation problem under a DSR.\n