Related papers: Value-at-Risk substitute for non-ruin capital is f…
With the growing interest in deploying robots in unstructured and uncertain environments, there has been increasing interest in factoring risk into safety-critical control development. Similarly, the authors believe risk should also be…
We introduce the concept of partial law invariance, generalizing the concepts of law invariance and probabilistic sophistication widely used in decision theory, as well as statistical and financial applications. This new concept is…
This paper introduces and studies factor risk measures. While risk measures only rely on the distribution of a loss random variable, in many cases risk needs to be measured relative to some major factors. In this paper, we introduce a…
It is shown that the axioms for coherent risk measures imply that whenever there is an asset in a portfolio that dominates the others in a given sample (which happens with finite probability even for large samples), then this portfolio…
The von Neumann and Morgenstern theory postulates that rational choice under uncertainty is equivalent to maximization of expected utility (EU). This view is mathematically appealing and natural because of the affine structure of the space…
Risk measures are important key figures to measure the adequacy of the reserves of a company. The most common risk measures in practice are Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). Recently, quantum-based algorithms are…
In this paper we characterise the propensity of big capital investments to systematically deliver poor outcomes as "fragility," a notion suggested by Nassim Taleb. A thing or system that is easily harmed by randomness is fragile. We argue…
This paper considers the ruin problem with random premiums, whose densities have rational Laplace transforms, and investments in a risky asset whose price follows a geometric Brownian motion. The asymptotic behavior of the ruin probability…
In this paper we discuss a general methodology to compute the market risk measure over long time horizons and at extreme percentiles, which are the typical conditions needed for estimating Economic Capital. The proposed approach extends the…
The paper concerns primal and dual representations as well as time consistency of set-valued dynamic risk measures. Set-valued risk measures appear naturally when markets with transaction costs are considered and capital requirements can be…
We introduce set risk measures (SRMs), real-valued maps defined on the family of non-empty closed bounded sets of essentially bounded random variables. SRMs extend traditional scalar risk measures by assigning a single capital requirement…
The time value of money is a critical factor not only in risk analysis, but also in insurance and financial applications. In this paper, we consider a special class of set-valued risk statistics by introducing the time value of money. In…
This paper firstly addresses the problem of risk assessment under false data injection attacks on uncertain control systems. We consider an adversary with complete system knowledge, injecting stealthy false data into an uncertain control…
We propose a generalization of the classical notion of the $V@R_{\lambda}$ that takes into account not only the probability of the losses, but the balance between such probability and the amount of the loss. This is obtained by defining a…
Multistage risk-averse optimal control problems with nested conditional risk mappings are gaining popularity in various application domains. Risk-averse formulations interpolate between the classical expectation-based stochastic and minimax…
The practice of valuation by marking-to-market with current trading prices is seriously flawed. Under leverage the problem is particularly dramatic: due to the concave form of market impact, selling always initially causes the expected…
Counterfactual explanations indicate the smallest change in input that can translate to a different outcome for a machine learning model. Counterfactuals have generated immense interest in high-stakes applications such as finance,…
Risk control has become one of the major concern of financial institutions. The need for adequate statistical tools to measure and anticipate the amplitude of the potential moves of financial markets is clearly expressed, in particular for…
Approximate Incremental Value-at-Risk formulae provide an easy-to-use preliminary guideline for risk allocation. Both the cases of risk adding and risk pooling are examined and beta-based formulae achieved. Results highlight how much the…
Value-at-risk is one of the important subjects that extensively used by researchers and practitioners for measuring and managing uncertainty in financial markets. Although value-at-risk is a common risk control instrument, but there are…