Time consistency of dynamic risk measures

2012 ◽  
Vol 40 (6) ◽  
pp. 436-439 ◽  
Author(s):  
Alexander Shapiro
Keyword(s):  
Risk Measures ◽  
Time Consistency ◽  
Dynamic Risk Measures ◽  
Dynamic Risk

scholarly journals Dynamic Risk Measures for Processes via Backward Stochastic Differential Equations Associated with Lévy Processes

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 741
Author(s):  
Liangliang Miao ◽  
Zhang Liu ◽  
Yijun Hu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Lévy Processes ◽  
Risk Measures ◽  
Time Consistency ◽  
Levy Processes ◽  
Backward Stochastic Differential Equations ◽  
Dynamic Risk Measures ◽  
Numerical Examples ◽  
Dynamic Risk

In this paper, we study the dynamic risk measures for processes induced by backward stochastic differential equations driven by Teugel’s martingales associated with Lévy processes (BSDELs). The representation theorem for generators of BSDELs is provided. Furthermore, the time consistency of the coherent and convex dynamic risk measures for processes is characterized by means of the generators of BSDELs. Moreover, the coherency and convexity of dynamic risk measures for processes are characterized by the generators of BSDELs. Finally, we provide two numerical examples to illustrate the proposed dynamic risk measures.

scholarly journals Pricing under dynamic risk measures

2019 ◽  
Vol 17 (1) ◽  
pp. 894-905 ◽  
Author(s):  
Jun Zhao ◽  
Emmanuel Lépinette ◽  
Peibiao Zhao
Keyword(s):  
Asset Pricing ◽  
Risk Measures ◽  
Time Consistency ◽  
Representation Formula ◽  
Contingent Claims ◽  
Contingent Claim ◽  
Weak Version ◽  
Dynamic Risk Measures ◽  
Discounted Cash Flow ◽  
Dynamic Risk

Abstract In this paper, we study the discrete-time super-replication problem of contingent claims with respect to an acceptable terminal discounted cash flow. Based on the concept of Immediate Profit, i.e., a negative price which super-replicates the zero contingent claim, we establish a weak version of the fundamental theorem of asset pricing. Moreover, time consistency is discussed and we obtain a representation formula for the minimal super-hedging prices of bounded contingent claims.

scholarly journals CONSTRUCTION AND APPLICATION OF THE CLASSIFICATION SCHEME OF DYNAMIC RISK MEASURES ESTIMATING

2016 ◽  
Vol 5 ◽  
pp. 67-80 ◽  
Author(s):  
Nataly Zrazhevska
Keyword(s):  
Value At Risk ◽  
Classification Scheme ◽  
Risk Measures ◽  
Estimation Method ◽  
Daily Basis ◽  
Stock Index ◽  
Dynamic Risk Measures ◽  
Dynamic Risk ◽  
Risk Managers

The most popular methods for dynamic risk measures – Value-at-Risk (VaR) and Conditional VaR (CVaR) estimating were analyzed, description and comparative analysis of the methods were fulfilled, recommendations on the use were given. Results of the research were presented in the form of a classification scheme of dynamic risk measures estimating that facilitates the choice of an estimation method. The GARCH-based models of dynamic risk measures VaR and CVaR evaluation for artificially generated series and two time series of log return on a daily basis of the most well-known Asian stock indexes Nikkey225 Stock Index and CSI30 were constructed to illustrate the effectiveness of the proposed scheme. A qualitative analysis of the proposed models was conducted. To analyze the quality of the dynamic VaR estimations the Cupets test and the Cristoffersen test were used. For CVaR estimations the V-test was used as quality test. The tests results confirm the high quality of obtained estimations. The proposed classification scheme of dynamic risk measures VaR and CVaR estimating may be useful for risk managers of different financial institutions.

scholarly journals A DYNAMIC MODEL OF CENTRAL COUNTERPARTY RISK

2018 ◽  
Vol 21 (08) ◽  
pp. 1850050
Author(s):  
TOMASZ R. BIELECKI ◽  
IGOR CIALENCO ◽  
SHIBI FENG
Keyword(s):  
Dynamic Model ◽  
Numerical Study ◽  
Risk Measures ◽  
Structure Model ◽  
Counterparty Risk ◽  
Dynamic Risk Measures ◽  
Credit Quality ◽  
Dynamic Risk ◽  
Risk Sensitive

We introduce a dynamic model of the default waterfall of derivatives central counterparties and propose a risk sensitive method for sizing the initial margin, and the default fund and its allocation among clearing members. Using a Markovian structure model of joint credit migrations, our evaluation of the default fund takes into account the joint credit quality of clearing members as they evolve over time. Another important aspect of the proposed methodology is the use of the time consistent dynamic risk measures for computation of the initial margin and the default fund. We carry out a comprehensive numerical study, where, in particular, we analyze the advantages of the proposed methodology and its comparison with the currently prevailing methods used in industry.

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