Proves existence of a strategy to minimize shortfall for game options.
problem Minimizing shortfall for game options in discrete time.
method Proves existence of a self-financing strategy.
result Existence of a self-financing strategy to minimize shortfall for game options in discrete time.
This paper describes an empirical study of shortfall optimization with Barra Extreme Risk. We compare minimum shortfall to minimum variance portfolios in the US, UK, and Japanese equity markets using Barra Style Factors (Value, Growth, Momentum, etc.). We show that minimizing shortfall generally improves performance ov…
We study shortfall risk minimization for American options with path dependent payoffs under proportional transaction costs in the Black--Scholes (BS) model. We show that for this case the shortfall risk is a limit of similar terms in an appropriate sequence of binomial models. We also prove that in the continuous time …
Study on optimal strategies for minimizing shortfall risk in game options.
problem Existence of optimal hedging strategies for shortfall risk in game options.
method Continuous time Black--Scholes model, finite and infinite exercise times.
result Optimal strategies exist for finite exercise times but not for all time intervals.
The issue of constructing a risk minimizing hedge under an additional almost-surely type constraint on the shortfall profile is examined. Several classical risk minimizing problems are adapted to the new setting and solved. In particular, the bankruptcy threat of optimal strategies appearing in the classical risk minim…
We study partial hedging for game options in markets with transaction costs bounded from below. More precisely, we assume that the investor's transaction costs for each trade are the maximum between proportional transaction costs and a fixed transaction costs. We prove that in the continuous time Black--Scholes (BS) mo…
New method for practical hedging under uncertainty in continuous time models.
problem High minimal superhedging price for practical use in continuous-time models.
method Relaxed hedging criterion based on acceptable shortfall risks, combining aggregation and convex dual representation theorems.
result Derivation of duality results for minimal price on discounted claims.
Paper studies utility maximization continuity under weak convergence.
problem Continuity of utility maximization value under weak convergence.
method Establishes sufficient conditions and weak convergence results.
result Computes minimal expected shortfall in the Heston model.
Risk measures for multivariate financial positions are studied in a utility-based framework. Under a certain incomplete preference relation, shortfall and divergence risk measures are defined as the optimal values of specific set minimization problems. The dual relationship between these two classes of multivariate ris…
New method optimizes risk estimation for financial losses.
problem Estimating expected shortfall risk for heavy-tailed distributions.
method Proposes a novel estimator for expected shortfall robust to data corruption.
result Demonstrates superior performance and robustness compared to classical methods.
Optimal tontine strategy maximizes withdrawals while minimizing shortfall.
problem Maximizing withdrawals from a tontine account with withdrawal constraints.
method Dynamic programming and Fourier methods to solve PIDE, tested with historical data.
result Tontine overlay strategy outperforms constant withdrawal strategies.
CAESar improves risk forecasting by combining VaR and ES estimates.
problem Lack of tail risk measures in financial risk management.
method Conditional Autoregressive Expected Shortfall model, combining VaR and ES estimates.
result CAESar outperforms existing methods in risk forecasting.
This paper attempts to provide a decision-theoretic foundation for the measurement of economic tail risk, which is not only closely related to utility theory but also relevant to statistical model uncertainty. The main result is that the only risk measures that satisfy a set of economic axioms for the Choquet expected …
Paper tackles liquidating stocks using reinforcement learning.
problem Liquidating large quantities of highly correlated stocks efficiently.
method Stochastic optimal control and reinforcement learning.
result Minimizes overall execution shortfall of stocks.
This paper proves Expected Shortfall is concave, not convex.
problem Understanding the convexity/concavity of Expected Shortfall.
method Analytical proof of concavity with respect to probability distributions.
result Expected Shortfall is concave, not convex.
New risk measures adjust for tail risk inadequacies.
problem Tail risk inadequacy in classical risk measures.
method Developed a family of adjusted risk measures using target risk profiles.
result Analyzed and derived properties of adjusted risk measures.
We shall provide in this paper good deal pricing bounds for contingent claims induced by the shortfall risk with some loss function. Assumptions we impose on loss functions and contingent claims are very mild. We prove that the upper and lower bounds of good deal pricing bounds are expressed by convex risk measures on …
Study on expectile and expected shortfall for tail risk assessment.
problem Comparing expectile and expected shortfall for tail risk assessment.
method Duality results and optimized certainty equivalent.
result Derived bounds and asymptotic behavior of expectile with respect to expected shortfall.
Simplifies study of multivariate shortfall risk measures.
problem Complexity in studying multivariate shortfall risk measures.
method Defines shortfall risk measures through a 1-dimensional function.
result Simplifies properties of multivariate shortfall risk measures.
Dual representation and properties of expectile-based expected shortfall studied.
problem Studying the expectile-based expected shortfall as a risk measure.
method Provided dual representation in terms of Bochner integral, showed boundedness properties, and computed for selected distributions.
result Explicit dual representation and boundedness properties of expectile-based expected shortfall.
New AI models improve financial hedging by reducing shortfall and tail risk.
problem Static model calibration gaps in derivatives markets.
method Two reinforcement learning frameworks: RLOP and QLBS.
result RLOP reduces shortfall frequency and improves tail risk in stress scenarios.
We offer a simplified proof for Expected Shortfall's dual representation.
problem The dual representation of Expected Shortfall.
method Basic properties of quantile functions.
result New proof of Expected Shortfall's subadditivity.
The paper calculates bounds for risk metrics and entropies under partial information constraints.
problem Analyzing risk metrics and entropies for unimodal, symmetric distributions with limited information.
method Develops lower and upper bounds for worst-case distortion riskmetrics and weighted entropy for unimodal, symmetric distributions with known mean and variance.
result Sharp upper bounds for distortion riskmetrics and weighted entropy for symmetric distributions.
We refine Expected Shortfall by controlling different tail portions, offering tailored risk assessments.
problem Risk assessment in financial positions, especially in tail regions.
method Introducing adjusted Expected Shortfall measures that control different tail portions.
result Adjusted Expected Shortfall measures ensure risk does not exceed specified thresholds for various probability levels.
Investigates a new measure PELVE_n for risk assessment.
problem Estimating higher-order risk measures in finance.
method Mathematical analysis and distribution-specific calculations.
result Developed and analyzed PELVE_n for various distributions.
Investigates risk measures for DC pension decumulation.
problem Develop optimal decumulation strategies for DC plan holders.
method Formulates decumulation as a control problem, studies risk measures (expected shortfall, linear shortfall, probability of shortfall).
result Optimal controls for expected reward and expected shortfall are identical to those for expected reward and linear shortfall.
Optimal retirement timing and consumption under shortfall risk management
problem Optimal portfolio, consumption, and endogenous early retirement problem
method Maximizing expected lifetime consumption utility while managing the maximum wealth shortfall relative to a benchmark
result Geometric structure of the stopping set and feedback-form optimal retirement boundary
The paper analyzes worst-case distortion risk metrics and weighted entropy under partial information.
problem Analyzing worst-case distortion risk metrics and weighted entropy with limited information.
method General distributions, partial information (mean and variance), various entropies and risk measures.
result Provides worst-case results for distortion risk metrics and weighted entropy.
This paper introduces new risk measures for evaluating losses with varying time horizons.
problem Capturing horizon risk and cash non-additivity in risk evaluation.
method Uses BSDEs and shortfall approaches to develop h-generalized shortfall risk measures.
result Introduces hq-entropic risk measures as a new family of fully-dynamic risk measures.
A new backtesting framework for Expected Shortfall simplifies risk measurement.
problem Backtesting Expected Shortfall for regulatory compliance.
method Combining risk and cash-flow into a secured position, using monotonicity of Expected Shortfall.
result A simple test statistic efficiently backtests Expected Shortfall.
In incomplete financial markets not every contingent claim can be replicated by a self-financing strategy. The risk of the resulting shortfall can be measured by convex risk measures, recently introduced by Föllmer, Schied (2002). The dynamic optimization problem of finding a self-financing strategy that minimizes the …
Study asymptotic properties of generalized shortfall risk measures for heavy-tailed risks.
problem Understanding risk measures for heavy-tailed risks.
method Derive asymptotic expansions for generalized shortfall risk measures.
result Unified theory for risk measures including distortion and utility-based measures.
The problem of estimation error of Expected Shortfall is analyzed, with a view of its introduction as a global regulatory risk measure.
We find the optimal investment strategy for an individual who seeks to minimize one of four objectives: (1) the probability that his wealth reaches a specified ruin level {\it before} death, (2) the probability that his wealth reaches that level {\it at} death, (3) the expectation of how low his wealth drops below a sp…
New framework forecasts ES using weighted quantiles.
problem Forecasting Expected Shortfall (ES) in financial markets.
method Two-step procedure: VaR estimation through quantile regressions, ES computation as weighted average.
result Proposed models outperform other methods in stock market indices forecasting.
Submodularity is studied for convex risk measures, including Expected Shortfall.
problem Characterizing submodularity in convex risk measures.
method Analyzing submodularity properties of law-invariant coherent risk measures, including Expected Shortfall and Value-at-Risk.
result AES is submodular only when it reduces to ES, and empirical analysis shows AES violations are less frequent than VaR and ES violations.
Introduces Lambda Expected Shortfall as a risk measure generalizing ES.
problem Lack of a comprehensive risk measure that generalizes ES and Lambda-VaR.
method Introduces Lambda-ES, a new risk measure with explicit formula and properties.
result Lambda-ES is the smallest quasi-convex and law-invariant risk measure dominating Lambda-VaR.
Expected Shortfall (ES) in several variants has been proposed as remedy for the defi-ciencies of Value-at-Risk (VaR) which in general is not a coherent risk measure. In fact, most definitions of ES lead to the same results when applied to continuous loss distributions. Differences may appear when the underlying loss di…
The paper introduces and studies hedging for game (Israeli) style extension of swing options considered as multiple exercise derivatives. Assuming that the underlying security can be traded without restrictions we derive a formula for valuation of multiple exercise options via classical hedging arguments. Introducing t…
We show that the shortfall risk of binomial approximations of game (Israeli) options converges to the shortfall risk in the corresponding Black--Scholes market considering Lipschitz continuous path-dependent payoffs for both discrete- and continuous-time cases. These results are new also for usual American style option…
We consider the pricing and hedging of exotic options in a model-independent set-up using \emph{shortfall risk and quantiles}. We assume that the marginal distributions at certain times are given. This is tantamount to calibrating the model to call options with discrete set of maturities but a continuum of strikes. In …
A new tail-shape index based on Value at Risk and Expected Shortfall.
problem Measuring and comparing tail behavior of loss distributions.
method Introducing a new θ-index based on equal level relationships between Value at Risk and Expected Shortfall. result The θ-index provides a level-dependent, scale-free measure of upper tail behavior. Financial institutions have to allocate so-called "economic capital" in order to guarantee solvency to their clients and counter parties. Mathematically speaking, any methodology of allocating capital is a "risk measure", i.e. a function mapping random variables to the real numbers. Nowadays "value-at-risk", which is d…
Quantum algorithm for dynamic asset allocation using expected shortfall.
problem Dynamic risk management in finance, especially tail risks.
method Quantum annealing algorithm in QUBO form for expected shortfall constraint.
result Quantum algorithm provides a faster solution for dynamic asset allocation.
Study improves accuracy of risk measures using advanced algorithms.
problem Computing accurate risk measures for financial losses.
method Nested stochastic approximation and multilevel acceleration.
result Established central limit theorems for estimation errors.
New approximations for Value at Risk and Expected Shortfall accounting for kurtosis.
problem Approximating Value at Risk and Expected Shortfall with positive skewness and kurtosis.
method Extensions of the Normal Power Approximation incorporating skewness and kurtosis.
result Improved precision for various loss distributions.
The ongoing concern about systemic risk since the outburst of the global financial crisis has highlighted the need for risk measures at the level of sets of interconnected financial components, such as portfolios, institutions or members of clearing houses. The two main issues in systemic risk measurement are the compu…
Study shows equivalence of four risk constraints in non-concave optimization problems.
problem Investigating risk constraints in non-concave optimization for financial companies.
method Analytical solutions for four risk constraints (ES, EDS, VaR, AVaR) under non-concave optimization.
result All four risk constraints lead to the same optimal solution, differing from concave optimization.