Related papers: Risk Concentration and Diversification: Second-Ord…
In general, underestimation of risk is something which should be avoided as far as possible. Especially in financial asset management, equity risk is typically characterized by the measure of portfolio variance, or indirectly by quantities…
Specialization and diversification are two major strategies that complex systems might exploit. Given a fixed amount of resources, the question is whether to invest this in elements that respond in a correlated manner to external…
In this paper we investigate the applicability of a recently introduced primal-dual splitting method in the context of solving portfolio optimization problems which assume the minimization of risk measures associated to different convex…
The assortment problem in revenue management is the problem of deciding which subset of products to offer to consumers in order to maximise revenue. A simple and natural strategy is to select the best assortment out of all those that are…
For discretisations of hyperbolic conservation laws, mimicking properties of operators or solutions at the continuous (differential equation) level discretely has resulted in several successful methods. While well-posedness for nonlinear…
We introduce and study the main properties of a class of convex risk measures that refine Expected Shortfall by simultaneously controlling the expected losses associated with different portions of the tail distribution. The corresponding…
A fruitful idea, when providing subdifferential formulae and dual representations for convex risk measures, is to make use of the conjugate duality theory in convex optimization. In this paper we underline the outstanding role played by the…
This paper develops a method to derive optimal portfolios and risk premia explicitly in a general diffusion model for an investor with power utility and a long horizon. The market has several risky assets and is potentially incomplete.…
New versions of the set-valued average value at risk for multivariate risks are introduced by generalizing the well-known certainty equivalent representation to the set-valued case. The first "regulator" version is independent from any…
This paper considers an insurer with two collaborating business lines that faces three critical decisions: (1) dividend payout, (2) reinsurance coverage, and (3) capital injection between the lines, in the presence of model uncertainty. The…
We propose a data-driven portfolio selection model that integrates side information, conditional estimation and robustness using the framework of distributionally robust optimization. Conditioning on the observed side information, the…
In a randomised clinical trial, when the result of the primary endpoint shows a significant benefit, the secondary endpoints are scrutinised to identify additional effects of the treatment. However, this approach entails a risk of…
We aim to design strategies for sequential decision making that adjust to the difficulty of the learning problem. We study this question both in the setting of prediction with expert advice, and for more general combinatorial decision…
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…
The paper provides a framework for the assessment and optimization of the total risk of complex distributed systems. The framework takes into account the risk of each agent, which may arise from heterogeneous sources, as well as the risk…
We consider infinite dimensional optimization problems motivated by the financial model called Arbitrage Pricing Theory. Using probabilistic and functional analytic tools, we provide a dual characterization of the super-replication cost.…
A classical result in risk measure theory states that every coherent risk measure has a dual representation as the supremum of certain expected value over a risk envelope. We study this topic in more detail. The related issues include: 1.…
In this paper, we propose a general bi-objective model for portfolio selection, aiming to maximize both a diversification measure and the portfolio expected return. Within this general framework, we focus on maximizing a diversification…
We present a general approach to the pricing of products in finance and insurance in the multi-period setting. It is a combination of the utility indifference pricing and optimal intertemporal risk allocation. We give a characterization of…
A framework for risk-averse optimization problems is introduced that is resilient to ambiguities in the true form of the underlying probability distribution. The focus is on problems with partial differential equations (PDEs) as…