CAPM, rewards, and empirical asset pricing with coherent risk

The paper has 2 main goals: 1. We propose a variant of the CAPM based on coherent risk. 2. In addition to the real-world measure and the risk-neutral measure, we propose the third one: the extreme measure. The introduction of this measure provides a powerful tool for investigating the relation between the first two measures. In particular, this gives us - a new way of measuring reward; - a new approach to the empirical asset pricing

Pricing and hedging in incomplete markets with coherent risk

We propose a pricing technique based on coherent risk measures, which enables one to get finer price intervals than in the No Good Deals pricing. The main idea consists in splitting a liability into several parts and selling these parts to different agents. The technique is closely connected with the convolution of coherent risk measures and equilibrium considerations. Furthermore, we propose a way to apply the above technique to the coherent estimation of the Greeks

Coherent measurement of factor risks

We propose a new procedure for the risk measurement of large portfolios. It employs the following objects as the building blocks: - coherent risk measures introduced by Artzner, Delbaen, Eber, and Heath; - factor risk measures introduced in this paper, which assess the risks driven by particular factors like the price of oil, S&P500 index, or the credit spread; - risk contributions and factor risk contributions, which provide a coherent alternative to the sensitivity coefficients. We also propose two particular classes of coherent risk measures called Alpha V@R and Beta V@R, for which all the objects described above admit an extremely simple empirical estimation procedure. This procedure uses no model assumptions on the structure of the price evolution. Moreover, we consider the problem of the risk management on a firm's level. It is shown that if the risk limits are imposed on the risk contributions of the desks to the overall risk of the firm (rather than on their outstanding risks) and the desks are allowed to trade these limits within a firm, then the desks automatically find the globally optimal portfolio

Exponential martingales and changes of measure for counting processes

We give sufficient criteria for the Dol\'eans-Dade exponential of a stochastic integral with respect to a counting process local martingale to be a true martingale. The criteria are adapted particularly to the case of counting processes and are sufficiently weak to be useful and verifiable, as we illustrate by several examples. In particular, the criteria allow for the construction of for example nonexplosive Hawkes processes as well as counting processes with stochastic intensities depending on diffusion processes

Robust pricing and hedging of double no-touch options

Double no-touch options, contracts which pay out a fixed amount provided an underlying asset remains within a given interval, are commonly traded, particularly in FX markets. In this work, we establish model-free bounds on the price of these options based on the prices of more liquidly traded options (call and digital call options). Key steps are the construction of super- and sub-hedging strategies to establish the bounds, and the use of Skorokhod embedding techniques to show the bounds are the best possible. In addition to establishing rigorous bounds, we consider carefully what is meant by arbitrage in settings where there is no {\it a priori} known probability measure. We discuss two natural extensions of the notion of arbitrage, weak arbitrage and weak free lunch with vanishing risk, which are needed to establish equivalence between the lack of arbitrage and the existence of a market model.Comment: 32 pages, 5 figure

Follow-Up After Hip and Knee Arthroplasty: a Review of the Literature and a Report on a Pilot Project at the Vreden National Medical Research Center of Traumatology and Orthopedics

Background. Today in our country, the follow-up of patients after arthroplasty is carried out in accordance with clinical guidelines, the wording of which is based on monographs from 2006, 2008, and 2014, in addition, clinical guidelines for follow-up do not take into account the results of treatment assessed by the patient himself. The purpose of this study was to examine existing systems and develop a proprietary follow-up system for patients after hip and knee arthroplasty. Results. A review of the literature revealed that follow-up of patients after arthroplasty is an unsolved problem, within which there is low coverage, reluctance or forgetfulness of the asymptomatic patient, the problem of accessibility of medical examinations, and an excessive financial burden on the health care system. Since 2022, fixed recommendations for follow-up after arthroplasty have been used in the clinical practice of our center in discharge epicrisis. Recommendations for the frequency of follow-up were formulated by experts based on a comprehensive review of the literature and their own experience. In the first three months, 221 hip and 235 knee evaluation questionnaires were collected through the proposed mechanism, with a progressive increase in the number of questionnaires based on weekly monitoring data. Conclusion. Unfortunately, the outpatient clinic system is not always able to provide qualitative monitoring of patients after arthroplasty due to various reasons, therefore, in our opinion, the implementation of the mechanism of remote monitoring of patients will allow detecting various complications at the stage of early diagnosis, which will contribute to prompt solution of these problems. The remote monitoring system is also an important source of scientific data

Meta-analysis Followed by Replication Identifies Loci in or near CDKN1B, TET3, CD80, DRAM1, and ARID5B as Associated with Systemic Lupus Erythematosus in Asians

Systemic lupus erythematosus (SLE) is a prototype autoimmune disease with a strong genetic involvement and ethnic differences. Susceptibility genes identified so far only explain a small portion of the genetic heritability of SLE, suggesting that many more loci are yet to be uncovered for this disease. In this study, we performed a meta-analysis of genome-wide association studies on SLE in Chinese Han populations and followed up the findings by replication in four additional Asian cohorts with a total of 5,365 cases and 10,054 corresponding controls. We identified genetic variants in or near CDKN1B, TET3, CD80, DRAM1, and ARID5B as associated with the disease. These findings point to potential roles of cell-cycle regulation, autophagy, and DNA demethylation in SLE pathogenesis. For the region involving TET3 and that involving CDKN1B, multiple independent SNPs were identified, highlighting a phenomenon that might partially explain the missing heritability of complex diseases

Pricing with coherent risk

This paper deals with applications of coherent risk measures to pricing in incomplete markets. Namely, we study the No Good Deals pricing technique based on coherent risk. Two forms of this technique are presented: one defines a good deal as a trade with negative risk; the other one defines a good deal as a trade with unusually high RAROC. For each technique, the fundamental theorem of asset pricing and the form of the fair price interval are presented. The model considered includes static as well as dynamic models, models with an infinite number of assets, models with transaction costs, and models with portfolio constraints. In particular, we prove that in a model with proportional transaction costs the fair price interval converges to the fair price interval in a frictionless model as the coefficient of transaction costs tends to zero. Moreover, we study some problems in the ``pure'' theory of risk measures: we present a simple geometric solution of the capital allocation problem and apply it to define the coherent risk contribution. The mathematical tools employed are probability theory, functional analysis, and finite-dimensional convex analysis.