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Register a new userShortfall Deviation Risk: An alternative to risk measurement
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We present the Shortfall Deviation Risk (SDR), a risk measure that represents the expected loss that occurs with certain probability penalized by the dispersion of results that are worse than such an expectation. SDR combines Expected Shortfall (ES) and Shortfall Deviation (SD), which we also introduce, contemplating two fundamental pillars of the risk concept, the probability of adverse events and the variability of an expectation, and considers extreme results. We demonstrate that SD is a generalized deviation measure, whereas SDR is a coherent risk measure. We achieve the dual representation of SDR, and we discuss issues such as its representation by a weighted ES, acceptance sets, convexity, continuity and the relationship with stochastic dominance. Illustrations with real and simulated data allow us to conclude that SDR offers greater protection in risk measurement compared with VaR and ES, especially in times of significant turbulence in riskier scenarios.
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We propose a method to assess the intrinsic risk carried by a financial position $X$ when the agent faces uncertainty about the pricing rule assigning its present value. Our approach is inspired by a new interpretation of the quasiconvex duality in a Knightian setting, where a family of probability measures replaces the single reference probability and is then applied to value financial positions. Diametrically, our construction of Value&Risk measures is based on the selection of a basket of claims to test the reliability of models. We compare a random payoff $X$ with a given class of derivatives written on $X$ , and use these derivatives to textquotedblleft testtextquotedblright the pricing measures. We further introduce and study a general class of Value&Risk measures $% R(p,X,mathbb{P})$ that describes the additional capital that is required to make $X$ acceptable under a probability $mathbb{P}$ and given the initial price $p$ paid to acquire $X$.
We shall provide in this paper good deal pricing bounds for contingent claims induced by the shortfall risk with some loss function. Assumptions we impose on loss functions and contingent claims are very mild. We prove that the upper and lower bounds of good deal pricing bounds are expressed by convex risk measures on Orlicz hearts. In addition, we obtain its representation with the minimal penalty function. Moreover, we give a representation, for two simple cases, of good deal bounds and calculate the optimal strategies when a claim is traded at the upper or lower bounds of its good deal pricing bound.
Since Claude Shannon founded Information Theory, information theory has widely fostered other scientific fields, such as statistics, artificial intelligence, biology, behavioral science, neuroscience, economics, and finance. Unfortunately, actuarial science has hardly benefited from information theory. So far, only one actuarial paper on information theory can be searched by academic search engines. Undoubtedly, information and risk, both as Uncertainty, are constrained by entropy law. Todays insurance big data era means more data and more information. It is unacceptable for risk management and actuarial science to ignore information theory. Therefore, this paper aims to exploit information theory to discover the performance limits of insurance big data systems and seek guidance for risk modeling and the development of actuarial pricing systems.
It has been for a long time to use big data of autonomous vehicles for perception, prediction, planning, and control of driving. Naturally, it is increasingly questioned why not using this big data for risk management and actuarial modeling. This article examines the emerging technical difficulties, new ideas, and methods of risk modeling under autonomous driving scenarios. Compared with the traditional risk model, the novel model is more consistent with the real road traffic and driving safety performance. More importantly, it provides technical feasibility for realizing risk assessment and car insurance pricing under a computer simulation environment.
The intuition of risk is based on two main concepts: loss and variability. In this paper, we present a composition of risk and deviation measures, which contemplate these two concepts. Based on the proposed Limitedness axiom, we prove that this resulting composition, based on properties of the two components, is a coherent risk measure. Similar results for the cases of convex and co-monotone risk measures are exposed. We also provide examples of known and new risk measures constructed under this framework in order to highlight the importance of our approach, especially the role of the Limitedness axiom.
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