Risk Measures and Attitudes by Francesca Biagini Andreas Richter & Harris Schlesinger

Author:Francesca Biagini, Andreas Richter & Harris Schlesinger
Language: eng
Format: epub
Publisher: Springer London, London

4.2 The General Setting

Let be a complete probability space. For a fixed time horizon T∈(0,∞), let be a filtration on satisfying the usual conditions of right-continuity and completeness. Let W=(W t )0≤t≤T be an ℝ d -valued Brownian motion on the filtered probability space . To allow for greater generality, we do not assume from the beginning that , meaning that the filtration may be strictly larger than the P-augmented Brownian filtration . Also, the initial σ-field may be strictly larger than the trivial σ-field.

We consider a financial market composed of N+1 securities S 0,S 1,…,S N , with N≤d. As usual, we let S 0 represent a locally riskless asset, which we name savings account, and we define the process as follows:

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