Dynamic risk measures for stochastic asset processes from ruin theory

AbstractThis article considers a dynamic version of risk measures for stochastic asset processes and gives a mathematical benchmark for required capital in a solvency regulation framework. Some dynamic risk measures, based on the expected discounted penalty function launched by Gerber and Shiu, are proposed to measure solvency risk from the company’s going-concern point of view. This study proposes a novel mathematical justification of a risk measure for stochastic processes as a map on a functional path space of future loss processes.

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SET-VALUED DYNAMIC RISK MEASURES FOR BOUNDED DISCRETE-TIME PROCESSES

International Journal of Theoretical and Applied Finance ◽

10.1142/s021902492050017x ◽

2020 ◽

Vol 23 (03) ◽

pp. 2050017

Author(s):

YANHONG CHEN ◽

YIJUN HU

Keyword(s):

Discrete Time ◽

Value At Risk ◽

Risk Measures ◽

Risk Measure ◽

Dynamic Risk Measures ◽

Time Value Of Money ◽

Average Value ◽

Dynamic Risk ◽

Entropic Risk Measure ◽

Average Value At Risk

In this paper, we study how to evaluate the risk of a financial portfolio, whose components may be dependent and come from different markets or involve more than one kind of currencies, while we also take into consideration the uncertainty about the time value of money. Namely, we introduce a new class of risk measures, named set-valued dynamic risk measures for bounded discrete-time processes that are adapted to a given filtration. The time horizon can be finite or infinite. We investigate the representation results for them by making full use of Legendre–Fenchel conjugation theory for set-valued functions. Finally, some examples such as the set-valued dynamic average value at risk and the entropic risk measure for bounded discrete-time processes are also given.

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REPRESENTATION OF BSDE-BASED DYNAMIC RISK MEASURES AND DYNAMIC CAPITAL ALLOCATIONS

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024914500320 ◽

2014 ◽

Vol 17 (05) ◽

pp. 1450032 ◽

Cited By ~ 8

Author(s):

EDUARD KROMER ◽

LUDGER OVERBECK

Keyword(s):

Risk Measures ◽

Risk Measure ◽

Static Case ◽

Coherent Risk Measures ◽

Dynamic Risk Measures ◽

Convex Risk Measures ◽

Coherent Risk ◽

Dynamic Risk ◽

Entropic Risk Measure ◽

Representation Result

In this paper, we provide a new representation result for dynamic capital allocations and dynamic convex risk measures that are based on backward stochastic differential equations (BSDEs). We derive this representation from a classical differentiability result for BSDEs and the full allocation property of the Aumann–Shapley allocation. The representation covers BSDE-based dynamic convex and dynamic coherent risk measures. The results are applied to derive a representation for the dynamic entropic risk measure. Our results are also applicable in a specific way to the static case, where we are able to derive a new representation result for static convex risk measures that are Gâteaux-differentiable.

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

EUREKA Physics and Engineering ◽

10.21303/2461-4262.2016.00162 ◽

2016 ◽

Vol 5 ◽

pp. 67-80 ◽

Cited By ~ 2

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.

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11 Dynamic risk measures

Stochastic Finance ◽

10.1515/9783110218053.456 ◽

2013 ◽

Keyword(s):

Risk Measures ◽

Dynamic Risk Measures ◽

Dynamic Risk

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A DYNAMIC MODEL OF CENTRAL COUNTERPARTY RISK

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024918500504 ◽

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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