Related papers: Mortality/longevity Risk-Minimization with or with…
We consider learning methods based on the regularization of a convex empirical risk by a squared Hilbertian norm, a setting that includes linear predictors and non-linear predictors through positive-definite kernels. In order to go beyond…
Estimating risk measures such as large loss probabilities and Value-at-Risk is fundamental in financial risk management and often relies on computationally intensive nested Monte Carlo methods. While Multi-Level Monte Carlo (MLMC)…
We address the problem of portfolio optimization under the simplest coherent risk measure, i.e. the expected shortfall. As it is well known, one can map this problem into a linear programming setting. For some values of the external…
We analyze multiline pricing and capital allocation in equilibrium no-arbitrage markets. Existing theories often assume a perfect complete market, but when pricing is linear, there is no diversification benefit from risk pooling and…
Evaluating quality-of-life (QoL) outcomes in populations with high mortality risk is complicated by truncation by death, since QoL is undefined for individuals who do not survive to the planned measurement time. We propose a framework that…
Rates of convergence for empirical risk minimizers have been well studied in the literature. In this paper, we aim to provide a complementary set of results, in particular by showing that after normalization, the risk of the empirical…
We investigate the quantification of demographic risk in a framework consistent with the market-consistent valuation imposed by Solvency II. We provide compact formulas for evaluating inflows and outflows of a portfolio of insurance…
Money-back guarantees (MBGs) are features of pooled retirement income products that address bequest concerns by ensuring the initial premium is returned through lifetime payments or, upon early death, as a death benefit to the estate. This…
Recently we developed a new framework in Hirz et al (2015) to model stochastic mortality using extended CreditRisk$^+$ methodology which is very different from traditional time series methods used for mortality modelling previously. In this…
We introduce \textit{basic inequalities} for first-order iterative optimization algorithms, forming a simple and versatile framework that connects implicit and explicit regularization. While related inequalities appear in the literature, we…
The optimization of large portfolios displays an inherent instability to estimation error. This poses a fundamental problem, because solutions that are not stable under sample fluctuations may look optimal for a given sample, but are, in…
With the rise of emerging risks, model uncertainty poses a fundamental challenge in the insurance industry, making robust pricing a first-order question. This paper investigates how insurers' robustness preferences shape competitive…
Small-area mortality estimation is inherently difficult, as random fluctuations from low death counts can obscure real geographic differences. We introduce a flexible model that borrows strength across age, space, and time to estimate…
Estimating lifetime probabilities of default (PDs) under IFRS~9 and CECL requires projecting point--in--time transition matrices over multiple years. A persistent weakness is that macroeconomic forecast errors compound across horizons,…
Portfolio selection in the periodic investment of securities modeled by a multivariate Merton model with dependent jumps is considered. The optimization framework is designed to maximize expected terminal wealth when portfolio risk is…
We study the almost-sure termination problem for probabilistic programs. First, we show that supermartingales with lower bounds on conditional absolute difference provide a sound approach for the almost-sure termination problem. Moreover,…
We consider the problem of minimizing a certainty equivalent of the total or discounted cost over a finite and an infinite time horizon which is generated by a Partially Observable Markov Decision Process (POMDP). The certainty equivalent…
We study a generic principal-agent problem in continuous time on a finite time horizon. We introduce a framework in which the agent is allowed to employ measure-valued controls and characterise the continuation utility as a solution to a…
The paper proposes a new approach to model risk measurement based on the Wasserstein distance between two probability measures. It formulates the theoretical motivation resulting from the interpretation of fictitious adversary of robust…
We study an optimal execution strategy for purchasing a large block of shares over a fixed time horizon. The execution problem is subject to a general price impact that gradually dissipates due to market resilience. We allow for general…