Related papers: How much is optimal reinsurance degraded by error?
Inconsistent values are commonly encountered in real-world applications, which can negatively impact data analysis and decision-making. While existing research primarily focuses on identifying the smallest removal set to resolve…
We study the posterior distribution of the Bayesian multiple change-point regression problem when the number and the locations of the change-points are unknown. While it is relatively easy to apply the general theory to obtain the…
Overparametrization often helps improve the generalization performance. This paper presents a dual view of overparametrization suggesting that downsampling may also help generalize. Focusing on the proportional regime $m\asymp n \asymp p$,…
Consider the classical problem of predicting the next bit in a sequence of bits. A standard performance measure is {\em regret} (loss in payoff) with respect to a set of experts. For example if we measure performance with respect to two…
The dual risk model is a popular model in finance and insurance, which is often used to model the wealth process of a venture capital or high tech company. Optimal dividends have been extensively studied in the literature for a dual risk…
In this paper we consider reinsurance or risk sharing from a macroeconomic point of view. Our aim is to find socially optimal reinsurance treaties. In our setting we assume that there are $n$ insurance companies each bearing a certain risk…
We investigate an optimal reinsurance problem for an insurance company facing a constant fixed cost when the reinsurance contract is signed. The insurer needs to optimally choose both the starting time of the reinsurance contract and the…
We study an optimal investment problem under default risk where related information such as loss or recovery at default is considered as an exogenous random mark added at default time. Two types of agents who have different levels of…
The effectiveness of using model sparsity as a priori information when solving linear inverse problems is studied. We investigate the reconstruction quality of such a method in the non-idealized case and compute some typical recovery errors…
We investigate the optimal investment-reinsurance problem for insurance company with partial information on the market price of the risk. Through the use of filtering techniques we convert the original optimization problem involving…
In this paper, we study the problem of expected utility maximization of an agent who, in addition to an initial capital, receives random endowments at maturity. Contrary to previous studies, we treat as the variables of the optimization…
Risk scores are simple classification models that let users make quick risk predictions by adding and subtracting a few small numbers. These models are widely used in medicine and criminal justice, but are difficult to learn from data…
Understanding how the optimal value of an optimisation problem changes when its input data is modified is an old question in mathematical optimisation. This paper investigates the computation of the optimal values of a family of (possibly…
Utility-Based Shortfall Risk (UBSR) is a risk metric that is increasingly popular in financial applications, owing to certain desirable properties that it enjoys. We consider the problem of estimating UBSR in a recursive setting, where…
Stochastic optimization problems often involve the expectation in its objective. When risk is incorporated in the problem description as well, then risk measures have to be involved in addition to quantify the acceptable risk, often in the…
In the hypothesis of rare loss events, the general expression of the policy value has been determined as a functional of the "expected frequency / loss severity" function and of the retention function. Exponential disutility has been chosen…
A minimax estimator has the minimum possible error ("risk") in the worst case. We construct the first minimax estimators for quantum state tomography with relative entropy risk. The minimax risk of non-adaptive tomography scales as…
This study is aimed at answering the famous question of how the approximation errors at each iteration of Approximate Dynamic Programming (ADP) affect the quality of the final results considering the fact that errors at each iteration…
This paper establishes the first analytical relationship between predictive model performance and loss ratio in insurance pricing. We derive a closed-form formula connecting the Pearson correlation between predicted and actual losses to…
The problems of optimally estimating a phase, a direction, and the orientation of a Cartesian frame (or trihedron) with general pure states are addressed. Special emphasis is put on estimation schemes that allow for inconclusive answers or…