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Sequential Monte Carlo samplers for capital allocation under copula-dependent risk models. (English) Zbl 1314.91241

Summary: In this paper we assume a multivariate risk model has been developed for a portfolio and its capital derived as a homogeneous risk measure. The Euler (or gradient) principle, then, states that the capital to be allocated to each component of the portfolio has to be calculated as an expectation conditional to a rare event, which can be challenging to evaluate in practice. We exploit the copula-dependence within the portfolio risks to design a Sequential Monte Carlo Samplers based estimate to the marginal conditional expectations involved in the problem, showing its efficiency through a series of computational examples.

MSC:

91G60 Numerical methods (including Monte Carlo methods)
91B30 Risk theory, insurance (MSC2010)
65C05 Monte Carlo methods
65C40 Numerical analysis or methods applied to Markov chains
62P05 Applications of statistics to actuarial sciences and financial mathematics

Software:

copula; HAC; QRM; LibBi; copula
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References:

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