We propose a deep reinforcement learning (RL) framework designed to optimize the hedging of specific, user-defined risk factors—referred to as targeted risks—in financial instruments affected by multiple sources of uncertainty. Our methodology uses Shapley value decompositions to establish source of risk grouping’s contribution to the projected contract cash flows, providing a clear attribution of the profit and loss to distinct risk categories. Leveraging this decomposition, we apply deep RL to hedge only the targeted risks, while leaving non-targeted risks mostly unaffected. In addition, we introduce a joint neural network architecture in which the agent network utilizes risk estimates from a risk measurement neural network to stabilize the hedging strategy, taking into account local risk dynamics. Numerical experiments show that our approach outperforms traditional methods, such as delta hedging and traditional deep hedging, significantly reducing targeted risks in variable annuities while maintaining flexibility for broader applications.

This paper studies an optimal reinsurance problem for a utility-maximizing insurer, subject to the reinsurer’s endogenous default and background risk. An endogenous default occurs when the insurer’s contractual indemnity exceeds the reinsurer’s available reserve, which is random due to the background risk. We obtain an analytical solution to the optimal contract for two types of reinsurance contracts, differentiated by whether their indemnity functions depend on the reinsurer’s background risk. The results shed light on the joint effect of the reinsurer’s default and background risk on the insurer’s reinsurance demand.

In this paper, we design a novel axiomatic approach to evaluating the joint risk of multiple insurance risks under dependence uncertainty. To be precise, we first establish a joint risk measure for non-negative multivariate risks, which we refer to as a (scalar) distortion joint risk measure. Then, we characterize it via a new set of axioms. Moreover, we introduce a new class of vector-valued distortion joint risk measures for non-negative multivariate risks and discuss their basic properties. Finally, comparisons with some existing vector-valued multivariate risk measures are made. It turns out that those vector-valued multivariate risk measures have forms of vector-valued distortion joint risk measures, respectively. This paper provides some relevant theoretical results about the evaluation of joint risk under dependence uncertainty.

Individual loss reserving methods have undergone substantial development in the past decade, driven by increased accessibility to granular-level insurance claims data. This paper presents a micro loss reserving model tailored for multi-coverage insurance policies, where a single insurance claim might trigger payments from multiple coverage types. We employ a copula-based multivariate regression approach to jointly model the settlement time and loss amount, effectively capturing the dependence among various types of loss amounts and their correlation with the settlement time. We stress the importance of considering both types of dependence for accurate reserving prediction and uncertainty quantification. Furthermore, we propose computationally efficient algorithms for parameter estimation and dynamic prediction. Through numerical experiments and real data analysis, we demonstrate the effectiveness of our proposed multivariate predictive model in loss reserving applications.

A novel family of statistical distributions, called enriched truncated exponentiated generalized family, is theoretically developed to model heavy-tailed data. One of the three-parameter sub-models of this family derived from log-logistic distribution is comprehensively studied. The statistical properties are explored, including moments and Fisher information matrix. In addition, tail-heaviness is studied using the tail-index approach. The method of maximum likelihood is used for parameter estimation, and existence and uniqueness of these estimators are shown. The flexibility of the new family is further validated by applying to the Norwegian fire insurance claim dataset. The goodness-of-fit measures are used to illustrate the adequacy of the proposed family of distributions. Furthermore, a backtesting procedure is conducted for well-known risk measures to assess the accuracy of the right tail fit.