We compare two different definitions of Tail-Value-at-Risk in multiperiod models: the wellknown backward recursive dynamically consistent definition (DTVaR), and the sequentially consistent version (STVaR), satisfying a weaker form of time consistency that only requires that acceptability levels do not exceed essential extremes later on. We extend the proposal for STVaR in Roorda and Schumacher (2007) to a more general setting, and indicate why STVaR is to be preferred if low levels (conditioning on tails with low probability) plays a role, as e.g. in a regulatory context. We show how the backward recursion in DTVaR can be restored for STVaR, to some extent, and indicate how this can be exploited in evaluation by Monte-Carlo simulation. We compare two different definitions of Tail-Value-at-Risk in multiperiod models: the wellknown backward recursive dynamically consistent definition (DTVaR), and the sequentially consistent version (STVaR), satisfying a weaker form of time consistency that only requires that acceptability levels do not exceed essential extremes later on. We indicate why STVaR is to be preferred if low levels (conditioning on tails with low probability) plays a role, as e.g. in a regulatory context. It is shown how the backward recursion in DTVaR can be restored for STVaR, to some extent, and we indicate how this can be exploited in evaluation by Monte-Carlo simulation.
[1]
Sina Tutsch.
Update rules for convex risk measures
,
2008
.
[2]
H. Föllmer,et al.
Convex risk measures and the dynamics of their penalty functions
,
2006
.
[3]
David Heath,et al.
Coherent multiperiod risk adjusted values and Bellman’s principle
,
2007,
Ann. Oper. Res..
[4]
Terry J. Lyons,et al.
Stochastic finance. an introduction in discrete time
,
2004
.
[5]
G. Pflug,et al.
Modeling, Measuring and Managing Risk
,
2008
.
[6]
Marco Frittelli,et al.
Dynamic convex risk measures
,
2004
.
[7]
H. Föllmer,et al.
Stochastic Finance: An Introduction in Discrete Time
,
2002
.
[8]
Berend Roorda,et al.
Time Consistency Conditions for Acceptability Measures, with an Application to Tail Value at Risk
,
2007
.