Related papers: Sharpening Shapley Allocation: from Basel 2.5 to F…
Given a reference risk measure, the risk budgeting is the portfolio where each asset contributes a predetermined amount to the total risk. We propose a novel approach, alternative to the ones proposed in the literature, for the calculation…
Game-theoretic attribution techniques based on Shapley values are used to interpret black-box machine learning models, but their exact calculation is generally NP-hard, requiring approximation methods for non-trivial models. As the…
For the past two decades investors have observed long memory and highly correlated behavior of asset classes that does not fit into the framework of Modern Portfolio Theory. Custom correlation and standard deviation estimators consider…
High precision analytical approximation is proposed for variance-covariance based risk allocation in a portfolio of risky assets. A general case of a single-period multi-factor Merton-type model with stochastic recovery is considered. The…
We consider an investment process that includes a number of features, each of which can be active or inactive. Our goal is to attribute or decompose an achieved performance to each of these features, plus a baseline value. There are many…
We formulate banks' capital optimization problem as a classic mean variance optimization, by leveraging an accurate linear approximation to the Shapely or Constrained Aumann-Shapley (CAS) allocation of max or nested max cost functions. This…
This paper revisits and extends the 2013 development by Rockafellar and Uryasev of the Risk Quadrangle (RQ) as a unified scheme for integrating risk management, optimization, and statistical estimation. The RQ features four…
A justification of the Basel liquidity formula for risk capital in the trading book is given under the assumption that market risk-factor changes form a Gaussian white noise process over 10-day time steps and changes to P&L are linear in…
Portfolio optimization has been a central problem in finance, often approached with two steps: calibrating the parameters and then solving an optimization problem. Yet, the two-step procedure sometimes encounter the "error maximization"…
This paper studies the robust optimal gain selection problem for financial trading systems, formulated within a \emph{double linear policy} framework, which allocates capital across long and short positions. The key objective is to…
Entropy based ideas find wide-ranging applications in finance for calibrating models of portfolio risk as well as options pricing. The abstracted problem, extensively studied in the literature, corresponds to finding a probability measure…
To meet the Basel II regulatory requirements for the Advanced Measurement Approaches in operational risk, the bank's internal model should make use of the internal data, relevant external data, scenario analysis and factors reflecting the…
The Shapley value provides a principled framework for fairly distributing rewards among participants according to their individual contributions. While prior work has applied this concept to data valuation in machine learning, existing…
Estimating the covariance of asset returns, i.e., the risk model, is a key component of financial portfolio construction and evaluation. Most risk modeling approaches produce a factor model that decomposes the asset variability into two…
In our previous paper, "A Unified Approach to Systemic Risk Measures via Acceptance Set" (\textit{Mathematical Finance, 2018}), we have introduced a general class of systemic risk measures that allow for random allocations to individual…
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 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…
In the world of modern financial theory, portfolio construction has traditionally operated under at least one of two central assumptions: the constraints are derived from a utility function and/or the multivariate probability distribution…
Banks are required to use long-term default probabilities (PDs) of their portfolios when calculating credit risk capital under internal ratings-based (IRB) models. However, the calibration models and historical data typically reflect…
We define and develop an approach for risk budgeting allocation - a risk diversification portfolio strategy - where risk is measured using a dynamic time-consistent risk measure. For this, we introduce a notion of dynamic risk contributions…