
on Risk Management 
By:  Pengyu Wei; Zuo Quan Xu 
Abstract:  This paper studies a meanrisk portfolio choice problem for logreturns in a continuoustime, complete market. This is a growthoptimal problem with risk control. The risk of logreturns is measured by weighted ValueatRisk (WVaR), which is a generalization of ValueatRisk (VaR) and Expected Shortfall (ES). We characterize the optimal terminal wealth up to the concave envelope of a certain function, and obtain analytical expressions for the optimal wealth and portfolio policy when the risk is measured by VaR or ES. In addition, we find that the efficient frontier is a concave curve that connects the minimumrisk portfolio with the growth optimal portfolio, as opposed to the vertical line when WVaR is used on terminal wealth. Our results advocate the use of meanWVaR criterion for logreturns instead of terminal wealth in dynamic portfolio choice. 
Date:  2021–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2112.14451&r= 
By:  Václav Brož; Evžen Kocenda 
Abstract:  We analyze link between mortgagerelated regulatory penalties levied on banks and the level of systemic risk in the U.S. banking industry. We employ a frequency decomposition of volatility spillovers (connectedness) to assess systemwide risk transmission with short, medium, and longterm dynamics. We find that after the possibility of a penalty is first announced to the public, longterm systemic risk among banks tends to increase. From the dynamic perspective, bank penalties represent an overlooked risk as they do not increase systemic risk immediately, but the risk accumulates and propagates over the longterm. In this respect, bank penalties resemble still waters that run deep. In contrast, a settlement with regulatory authorities leads to a decrease in the longterm systemic risk. Our analysis is robust with respect to a number of relevant criteria. 
Keywords:  bank, global financial crisis, mortgage penalty, systemic risk, financial stability 
JEL:  C14 C58 G14 G21 G28 K41 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:ces:ceswps:_9463&r= 
By:  Riccardo Lucchetti (Dipartimento di Scienze Economiche e Sociali  Universita' Politecnica delle Marche); Mihaela Nicolau (Department of Finance and Accounting, Danubius University, Romania); Giulio Palomba (Dipartimento di Scienze Economiche e Sociali  Universita' Politecnica delle Marche); Luca Riccetti (Dipartimento di Economia e Diritto, Universita' di Macerata, Macerata, Italy) 
Abstract:  This article investigates the riskreturn relationship of managed portfolios when two risk indicators, the Tracking Error Volatility (TEV) and the ValueatRisk (VaR), are both constrained not to exceed preset maximum values. While in some cases these constraints may not be mutually compatible, it is often possible to find portfolios that satisfy both constraints. In this paper, we analyze the problem of choosing among these. Focusing on the tradeoff between the joint restrictions that can be imposed on both risk indicators, we de ne the Risk Balancing Frontier (RBF), a new portfolio boundary in the traditional absolute risktotal return space, that contains all the portfolios characterized by the minimum VaR attainable for each TEV level. We show that the RBF is the set of all tangency portfolios between two wellknown frontiers: the socalled Constrained Tracking Error Volatility Frontier (Jorion, 2003) and the Constrained ValueatRisk Frontier (Alexander and Baptista, 2008). Thus, the RBF is useful for analyzing the agency problem in delegated portfolio management. The RBF does not have a closedform de nition and must be determined numerically: to this aim, we develop a fast and accurate algorithm. 
Keywords:  Benchmarking, portfolio frontiers, tracking error volatility, ValueatRisk, misalignment of objectives 
JEL:  C61 G11 
Date:  2022–01 
URL:  http://d.repec.org/n?u=RePEc:anc:wpaper:461&r= 
By:  Viet Anh Nguyen; Soroosh Shafieezadeh Abadeh; Damir Filipovi\'c; Daniel Kuhn 
Abstract:  We introduce a universal framework for meancovariance robust risk measurement and portfolio optimization. We model uncertainty in terms of the Gelbrich distance on the meancovariance space, along with prior structural information about the population distribution. Our approach is related to the theory of optimal transport and exhibits superior statistical and computational properties than existing models. We find that, for a large class of risk measures, meancovariance robust portfolio optimization boils down to the Markowitz model, subject to a regularization term given in closed form. This includes the finance standards, valueatrisk and conditional valueatrisk, and can be solved highly efficiently. 
Date:  2021–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2112.09959&r= 
By:  Tobias Fissler; Michael Merz; Mario V. W\"uthrich 
Abstract:  A main difficulty in actuarial claim size modeling is that there is no simple offtheshelf distribution that simultaneously provides a good distributional model for the main body and the tail of the data. In particular, covariates may have different effects for small and for large claim sizes. To cope with this problem, we introduce a deep composite regression model whose splicing point is given in terms of a quantile of the conditional claim size distribution rather than a constant. To facilitate Mestimation for such models, we introduce and characterize the class of strictly consistent scoring functions for the triplet consisting a quantile, as well as the lower and upper expected shortfall beyond that quantile. In a second step, this elicitability result is applied to fit deep neural network regression models. We demonstrate the applicability of our approach and its superiority over classical approaches on a real accident insurance data set. 
Date:  2021–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2112.03075&r= 
By:  Jianming Xia 
Abstract:  A risk measure that is consistent with the secondorder stochastic dominance and additive for sums of independent random variables can be represented as a weighted entropic risk measure (WERM). The expected utility maximization problem with risk controlled by WERM and a related risk minimization problem are investigated in this paper. The latter is same to a problem of maximizing a weighted average of constantabsoluteriskaversion (CARA) certainty equivalents. The solutions of all the optimization problems are explicitly characterized and an iterative method of the solutions is provided. 
Date:  2021–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2112.02284&r= 
By:  Claudio Fontana; Alessandro Gnoatto; Guillaume Szulda 
Abstract:  We develop a stochastic volatility framework for modeling multiple currencies based on CBItimechanged L\'evy processes. The proposed framework captures the typical risk characteristics of FX markets and is coherent with the symmetries of FX rates. Moreover, due to the selfexciting behavior of CBI processes, the volatilities of FX rates exhibit selfexciting dynamics. By relying on the theory of affine processes, we show that our approach is analytically tractable and that the model structure is invariant under a suitable class of riskneutral measures. A semiclosed pricing formula for currency options is obtained by Fourier methods. We propose two calibration methods, also by relying on deeplearning techniques, and show that a simple specification of the model can achieve a good fit to market data on a currency triangle. 
Date:  2021–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2112.02440&r= 
By:  Antoine Jacquier; Aitor Muguruza; Alexandre Pannier 
Abstract:  We provide explicit smalltime formulae for the atthemoney implied volatility, skew and curvature in a large class of models, including rough volatility models and their multifactor versions. Our general setup encompasses both European options on a stock and VIX options, thereby providing new insights on their joint calibration. The tools used are essentially based on Malliavin calculus for Gaussian processes. We develop a detailed theoretical and numerical analysis of the twofactor rough Bergomi model and provide insights on the interplay between the different parameters for joint SPXVIX smile calibration. 
Date:  2021–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2112.14310&r= 
By:  Ling Wang; Mei Choi Chiu; Hoi Ying Wong 
Abstract:  This paper investigates the timeconsistent meanvariance reinsuranceinvestment (RI) problem faced by life insurers. Inspired by recent findings that mortality rates exhibit longrange dependence (LRD), we examine the effect of LRD on RI strategies. We adopt the Volterra mortality model proposed in Wang et al.(2021) to incorporate LRD into the mortality rate process and describe insurance claims using a compound Poisson process with the intensity represented by stochastic mortality rate. Under the openloop equilibrium meanvariance criterion, we derive explicit equilibrium RI controls and study the uniqueness of these controls in cases of constant and statedependent risk aversion. We simultaneously resolve difficulties arising from unbounded nonMarkovian parameters and sudden increases in the insurer's wealth process. We also use a numerical study to reveal the influence of LRD on equilibrium strategies. 
Date:  2021–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2112.06602&r= 
By:  Karun Adusumilli 
Abstract:  This paper provides a decision theoretic analysis of bandit experiments. The bandit setting corresponds to a dynamic programming problem, but solving this directly is typically infeasible. Working within the framework of diffusion asymptotics, we define a suitable notion of asymptotic Bayes risk for bandit settings. For normally distributed rewards, the minimal Bayes risk can be characterized as the solution to a nonlinear secondorder partial differential equation (PDE). Using a limit of experiments approach, we show that this PDE characterization also holds asymptotically under both parametric and nonparametric distribution of the rewards. The approach further describes the state variables it is asymptotically sufficient to restrict attention to, and therefore suggests a practical strategy for dimension reduction. The upshot is that we can approximate the dynamic programming problem defining the bandit setting with a PDE which can be efficiently solved using sparse matrix routines. We derive nearoptimal policies from the numerical solutions to these equations. The proposed policies substantially dominate existing methods such Thompson sampling. The framework also allows for substantial generalizations to the bandit problem such as time discounting and pure exploration motives. 
Date:  2021–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2112.06363&r= 
By:  Guijin Son; Joocheol Kim 
Abstract:  The BlackScholes model, defined under the assumption of a perfect financial market, theoretically creates a flawless hedging strategy allowing the trader to evade risks in a portfolio of options. However, the concept of a "perfect financial market," which requires zero transaction and continuous trading, is challenging to meet in the real world. Despite such widely known limitations, academics have failed to develop alternative models successful enough to be longestablished. In this paper, we explore the landscape of Deep Neural Networks(DNN) based hedging systems by testing the hedging capacity of the following neural architectures: Recurrent Neural Networks, Temporal Convolutional Networks, Attention Networks, and Span MultiLayer Perceptron Networks. In addition, we attempt to achieve even more promising results by combining traditional derivative hedging models with DNN based approaches. Lastly, we construct \textbf{NNHedge}, a deep learning framework that provides seamless pipelines for model development and assessment for the experiments. 
Date:  2021–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2112.10084&r= 
By:  Sergey Ivashchenko (The NorthWestern Main Branch of the Bank of Russia; The Institute of Regional Economy Studies (Russian Academy of Sciences); The Financial Research Institute); Semih Emre Cekin (Department of Economics, TurkishGerman University, Istanbul, Turkey); Rangan Gupta (Department of Economics, University of Pretoria, Private Bag X20, Hatfield 0028, South Africa) 
Abstract:  Recent research shows that timevarying volatility plays a crucial role in nonlinear modeling. Contributing to this literature, we suggest a DSGEGARCH approach that allows for straightforward computation of DSGE models with timevarying volatility. As an application of our approach, we examine the forecasting performance of the DSGEGARCH model using Eurozone realtime data. Our findings suggest that the DSGEGARCH approach is superior in outofsample forecasting performance in comparison to various other benchmarks for the forecast of inflation rates, output growth and interest rates, especially in the short term. Comparing our approach to the widely used stochastic volatility specification using insample forecasts, we also show that the DSGEGARCH is superior in insample forecast quality and computational effciency. In addition to these results, our approach reveals interesting properties and dynamics of timevarying correlations (conditional correlations). 
Keywords:  DSGE, forecasting, GARCH, stochastic volatility, conditional correlations 
JEL:  C32 E30 E37 
Date:  2022–01 
URL:  http://d.repec.org/n?u=RePEc:pre:wpaper:202204&r= 
By:  Jian Kang (School of Finance, Dongbei University of Finance and Economics); Johan Stax Jakobsen (Copenhagen Business School and CREATES); Annastiina Silvennoinen (NCER, Queensland University of Technology); Timo Teräsvirta (Aarhus University, CREATES, C.A.S.E, HumboldtUniversität zu Berlin); Glen Wade (NCER, Queensland University of Technology) 
Abstract:  We construct a parsimonious test of constancy of the correlation matrix in the multivariate conditional correlation GARCH model, where the GARCH equations are timevarying. The alternative to constancy is that the correlations change deterministically as a function of time. The alternative is a covariance matrix, not a correlation matrix, so the test may be viewed as a general test of stability of a constant correlation matrix. The size of the test in finite samples is studied by simulation. An empirical example is given. 
Keywords:  Deterministically varying correlation, multiplicative timevarying GARCH, multivariate GARCH, nonstationary volatility, smooth transition GARCH 
JEL:  C32 C52 C58 
Date:  2022–01–01 
URL:  http://d.repec.org/n?u=RePEc:aah:create:202201&r= 