Optimal Reinsurance with Multivariate Risks and Dependence Uncertainty
This paper explores the optimal #reinsurance design for an #insurer with multiple lines of business, where the dependence structure between #risks is unknown. The study considers Value-at-Risk (#var) and Range-Value-at-Risk (#rvar) as #riskmeasures and applies general premium principles. The optimal reinsurance strategies are obtained under budget constraint and expected profit constraint. Lire
Bayesian Mixed-Frequency Quantile Vector Autoregression: Eliciting Tail Risks of Monthly Us GDP
This paper proposes a novel mixed-frequency quantile vector autoregression (MF-QVAR) model that uses a #bayesian framework and multivariate asymmetric Laplace distribution to estimate missing low-frequency variables at higher frequencies. The proposed method allows for timely policy interventions by analyzing conditional quantiles for multiple variables of interest and deriving quantile-related #riskmeasures at high frequency. The model is applied to the […]
Stressing Dynamic Loss Models
“… we propose a reverse stress testing framework for dynamic models. Specifically, we consider a compound Poisson process over a finite time horizon and stresses composed of expected values of functions applied to the process at the terminal time. We then define the stressed model as the probability measure under which the process satisfies the […]
Assessing the difference between integrated quantiles and integrated cumulative distribution functions
“When developing large-sample statistical inference for quantiles, also known as Values-at-Risk in finance and insurance, the usual approach is to convert the task into sums of random variables. The conversion procedure requires that the underlying cumulative distribution function (cdf) would have a probability density function (pdf), plus some minor additional assumptions on the pdf. In […]
Evaluation of Backtesting on Risk Models Based on Data Envelopment Analysis
“The methodologies examined include filtered historical simulation, extreme value theory, Monte Carlo simulation and historical simulation. Autoregressive-moving-average and generalized-autoregressive-conditional-heteroscedasticity models are used to estimate VaR. “ Lire
Modeling Multivariate Operational Losses Via Copula-Based Distributions with G-and-H Marginals
“The empirical evidence suggests that a distribution based on a single copula is not flexible enough, and thus we model the dependence structure by means of vine copulas. We show that the approach based on regular vines improves the fit. Moreover, even though losses corresponding to different event types are found to be dependent, the […]
Distributionally Robust Reinsurance with Value-at-Risk and Conditional Value-at-Risk
“Our model handles typical stop-loss reinsurance contracts. We show that a three-point distribution achieves the worst-case VaR of the total retained loss of the insurer, from which the closed-form solutions of the worst-case distribution and optimal deductible are obtained. Moreover, we show that the worst-case Conditional Value-at-Risk of the total retained loss of the insurer is equal to the worst-case VaR, […]
Pareto-optimal Reinsurance Under Individual Risk Constraints
“This paper studies the design of Pareto-optimal reinsurance contracts in a market where the insurer and reinsurer maximize their expected utilities of end-of-period wealth. In addition, we assume that the insurer and reinsurer wish to control their solvency risks, which are defined through distortion risk measures of their end-of-period risk exposures.” Lire