Related papers: A decomposition of general premium principles into…
This paper studies an optimal insurance contracting problem in which the preferences of the decision maker given by the sum of the expected loss and a convex, increasing function of a deviation measure. As for the deviation measure, our…
The net-premium principle is considered to be the most genuine and fair premium principle in actuarial applications. However, an insurance company, applying the net-premium principle, goes bankrupt with probability one in the long run, even…
We propose a method to assess the intrinsic risk carried by a financial position $X$ when the agent faces uncertainty about the pricing rule assigning its present value. Our approach is inspired by a new interpretation of the quasiconvex…
A risk analyst assesses potential financial losses based on multiple sources of information. Often, the assessment does not only depend on the specification of the loss random variable but also various economic scenarios. Motivated by this…
We develop a general theory of risk measures that determines the optimal amount of capital to raise and invest in a portfolio of reference traded securities in order to meet a pre-specified regulatory requirement. The distinguishing feature…
We review the nature of some well-known phenomena such as volatility smiles, convexity adjustments and parallel derivative markets. We propose that the market is incomplete and postulate the existence of intrinsic risks in every contingent…
The risk premium is one of main concepts in mathematical finance. It is a measure of the trade-offs investors make between return and risk and is defined by the excess return relative to the risk-free interest rate that is earned from an…
In this paper, we consider the problem of optimal reinsurance design, when the risk is measured by a distortion risk measure and the premium is given by a distortion risk premium. First, we show how the optimal reinsurance design for the…
In the past decades, advanced probabilistic methods have had significant impact on the field of finance, both in academia and in the financial industry. Conversely, financial questions have stimulated new research directions in probability.…
Due to their heterogeneity, insurance risks can be properly described as a mixture of different fixed models, where the weights assigned to each model may be estimated empirically from a sample of available data. If a risk measure is…
The intuition of risk is based on two main concepts: loss and variability. In this paper, we present a composition of risk and deviation measures, which contemplate these two concepts. Based on the proposed Limitedness axiom, we prove that…
We study large and moderate deviations for a life insurance portfolio, without assuming identically distributed losses. The crucial assumption is that losses are bounded, and that variances are bounded below. From a standard large…
We study combinations of risk measures under no restrictive assumption on the set of alternatives. We develop and discuss results regarding the preservation of properties and acceptance sets for the combinations of risk measures. One of the…
The risk premium of a policy is the sum of the pure premium and the risk loading. In the classification ratemaking process, generalized linear models are usually used to calculate pure premiums, and various premium principles are applied to…
De Finetti's optimal reinsurance is a set of contracts, one for each risk in a portfolio, that caps the retained aggregate variance to a pre-specified level while minimizing total expected loss. The premiums are determined using the…
We present an approach to the dynamic valuation of exposure risks in the multi-period setting, which incorporates a dynamic and multiple diversification of risks in Pareto optimal sense. This approach extends classical indifference premium…
In the literature, insurance and reinsurance pricing is typically determined by a premium principle, characterized by a risk measure that reflects the policy seller's risk attitude. Building on the work of Meyers (1980) and Chen et al.…
Risk-neutral pricing dictates that the discounted derivative price is a martingale in a measure equivalent to the economic measure. The residual ambiguity for incomplete markets is here resolved by minimising the entropy of the price…
This paper studies optimal insurance design under asymmetric information in a Stackelberg framework, where a monopolistic insurer faces uncertainty about both the insured's risk attitude, captured by a risk-aversion parameter, and the…
In this article, we propose a novel characterization of law-invariant and coherent risk measures, based on a generalized optimal transport problem in which the second marginal of the admissible plans is not fixed, but required to lie within…