Set-valued average value at risk and its computation. (English) Zbl 1269.91071
Summary: New versions of the set-valued average value at risk for multivariate risks are introduced by generalizing the well-known certainty equivalent representation to the set-valued case. The first ‘regulator’ version is independent from any market model whereas the second version, called the market extension, takes trading opportunities into account. Essential properties of both versions are proven and an algorithmic approach is provided which admits to compute the values of both versions over finite probability spaces. Several examples illustrate various features of the theoretical constructions.
MSC:
| 91G10 | Portfolio theory |
| 26E25 | Set-valued functions |
| 91B60 | Trade models |
| 90C39 | Dynamic programming |
| 91G30 | Interest rates, asset pricing, etc. (stochastic models) |
Keywords:
average value at risk; set-valued risk measures; coherent risk measures; transaction costs; Benson’s algorithmSoftware:
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