MULTIDIMENSIONAL DYNAMIC RISK MEASURE VIA CONDITIONALg-EXPECTATION

AbstractWe consider an investor facing a classical portfolio problem of optimal investment in a log-Brownian stock and a fixed-interest bond, but constrained to choose portfolio and consumption strategies that reduce a dynamic shortfall risk measure. For continuous- and discrete-time financial markets we investigate the loss in expected utility of intermediate consumption and terminal wealth caused by imposing a dynamic risk constraint. We derive the dynamic programming equations for the resulting stochastic optimal control problems and solve them numerically. Our numerical results indicate that the loss of portfolio performance is not too large while the risk is notably reduced. We then investigate time discretization effects and find that the loss of portfolio performance resulting from imposing a risk constraint is typically bigger than the loss resulting from infrequent trading.

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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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Desistance From Sexual and Other Violent Offending Among Child Sexual Abusers

Criminal Justice and Behavior ◽

10.1177/0093854816670194 ◽

2016 ◽

Vol 44 (3) ◽

pp. 416-431 ◽

Cited By ~ 3

Author(s):

Michael P. Lasher ◽

Robert J. McGrath

Keyword(s):

Sex Offenders ◽

Sex Offender ◽

Risk Measure ◽

Offender Treatment ◽

First Year ◽

Sex Offender Treatment ◽

Community Reentry ◽

Dynamic Risk ◽

Violent Offending ◽

Child Sexual Abusers

Most sex offenders appear to desist from sexual and other violent offending; however, research on this population has historically focused more on the characteristics of individuals who persist offending versus those who desist from offending. The present study examined change patterns of 563 child sexual abusers’ scores on the Sex Offender Treatment Intervention and Progress Scale, a dynamic risk measure, at three points of time over 2 years. Individuals who did versus did not commit a new serious offense, defined as a new sexual or other violent offense, at 5-year follow-up were contrasted. Desisters demonstrated most changes during their first year in treatment, whereas change among persisters more often occurred during their second year in treatment. All classes of offenders made gains in addressing dynamic risk related to sexually specific needs, whereas desisters made significantly greater gains in social stability needs. Findings are discussed in light of treatment dose allocation and community reentry needs.

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Predicting Women’s Recidivism Using the Dynamic Risk Assessment for Offender Re-Entry: Preliminary Evidence of Predictive Validity With Community-Sentenced Women Using a “Gender-Neutral” Risk Measure

Criminal Justice and Behavior ◽

10.1177/0093854819896387 ◽

2020 ◽

Vol 47 (3) ◽

pp. 251-270

Author(s):

Jessica M. Scanlan ◽

Julia A. Yesberg ◽

Clare-Ann Fortune ◽

Devon L. L. Polaschek

Keyword(s):

Risk Factors ◽

Risk Assessment ◽

Predictive Validity ◽

Assessment Tool ◽

Risk Measure ◽

Assessment Tools ◽

Community Supervision ◽

Dynamic Risk ◽

Gender Neutral ◽

Dynamic Risk Assessment

Although men and women share risk factors for offending, some scholars suggest these factors operate differently across gender and that women-specific risk factors are neglected in existing “gender-neutral” risk assessment tools. This article explored the predictive validity of one gender-neutral risk assessment tool—the Dynamic Risk Assessment for Offender Re-Entry (DRAOR)—with matched samples of women and men serving community supervision sentences. Total DRAOR scores had comparative predictive validity across gender. For women and men, the DRAOR predicted reconviction over a static risk measure. The findings support the general premise of gender neutrality, but do not necessarily suggest the DRAOR, or gender-neutral tools more broadly, are the best tools for use with women.

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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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Dynamic risk measures for stochastic asset processes from ruin theory

Annals of Actuarial Science ◽

10.1017/s1748499518000064 ◽

2018 ◽

Vol 12 (2) ◽

pp. 249-268 ◽

Cited By ~ 1

Author(s):

Yasutaka Shimizu ◽

Shuji Tanaka

Keyword(s):

Risk Measures ◽

Risk Measure ◽

Point Of View ◽

Dynamic Risk Measures ◽

Expected Discounted Penalty Function ◽

Dynamic Risk ◽

Discounted Penalty Function ◽

Dynamic Version ◽

Future Loss ◽

Mathematical Justification

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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