SCRO / Journées de l'optimisation
HEC Montréal, 2931 mai 2023
CORSJOPT2023
HEC Montréal, 29 — 31 mai 2023
RM Risk Management
31 mai 2023 10h30 – 12h10
Salle: Procter & Gamble (vert)
Présidée par Ahmadreza Tavasoli
4 présentations

10h30  10h55
A relative robust approach on expected returns with bounded CVaR for portfolio selection
A robust optimization model to find a stable investment portfolio is proposed under twofold uncertainty sources: the random nature of returns for a given economic scenario which is in itself unknown. Our model combines expected returns together with risk and regret measures in order to find a solution ensuring acceptable returns while the investor is protected from the market volatility . More formally, we formulate a model that minimizes the maximum regret on the expected returns while the conditional valueatrisk is upper bounded under different scenario settings. Several mathematical formulations are analyzed. Duality relations drive us to obtaining bounds on the optimal objective value of the problem in order to develop a cutting plane approach. We show experimentally that, despite the large number (hundreds of thousands) of constraints and variables of the resulting problem, an optimal portfolio can be found in a few seconds. Finally, our model is tested in a financial decision making environment by simulating its application in different markets indexes and under different underlying economic conditions. It will be seen that using scenarios usually improves the realized portfolio returns.
Portfolio optimization, regret decisionmaking.

10h55  11h20
Counterfeit Detection over Ecommerce Platforms
Online sellers often sell counterfeit products over ecommerce platforms. We compare scenarios where different parties take actions to detect counterfeits and penalize the seller. Our research reveals some interesting managerial insights for the platforms and the regulators. We find that factors such as the relative quality of the counterfeit product compared to its original version and the effectiveness of detecting counterfeit product impact the counterfeit detection efforts by different parties. We find that under certain scenarios, the efforts by the platform are higher as compared to social planner. Finally, we find that under certain conditions, it is beneficial for the platform that the social planner takes anticounterfeit actions.

11h20  11h45
Cooperative Investment for Contagion Risk Mitigation: A Comparative Study of Multiple LowRisk Firms in Competitive Environments
Contagion risk, defined as the potential for an adverse event or shock to spread from one firm or sector to another, is a key concern in risk management. Previous studies have shown that lowrisk firms can profitably mitigate contagion risk by investing in a rival firm's safety measures. However, these studies have typically assumed the existence of only one lowrisk and one highrisk firm, which is limiting. This study investigates the potential for cooperative investment strategies to benefit multiple lowrisk firms facing multiple highrisk rivals and explores the conditions under which such investment is profitable. Specifically, we compare models of price and quantity competition among firms within an industry. Our findings highlight the significance of cooperative investment as a contagion risk mitigation strategy in competitive environments. The results of this study have important implications for operations risk management in industries susceptible to contagion risk.

11h45  12h10
Counterparty risk under netting agreements: A dynamic game interpretation
Counterparty risk is the risk of incurring losses from a portfolio of derivative contracts in the event of counterparty default. This risk depends on the default probability, as well as on the value of the derivatives. Credit netting is commonly used by financial institutions to mitigate counterparty risk. Under a netting agreement, contracts between two parties are combined into a netting portfolio. In case of default by one of the parties, financial obligations are netted.
In practice, netting portfolios often contain derivatives allowing for early exercise opportunities (e.g. Bermudan options). The composition of the netted portfolio varies with time, as some of the options mature or are exercised by their respective holders.
In this paper, we show that credit risk and netting agreements have a significant impact on the way portfolios are managed (that is, on their exercise strategies) and, therefore, on the value of the portfolio and on the price of counterparty risk. We establish that, under a netting agreement, the expected payoffs of counterparties depend on their joint exercise strategy. We derive the value of a netted portfolio as the Nash equilibrium solution of a zerosum, finite horizon, discretetime stochastic game.
We show that this dynamicgame interpretation can be used to determine the value of the regulatory capital charges required of financial institutions to cover for counterparty credit risk (credit valuation adjustment or bilateral valuation adjustment). These adjustments are evaluated by comparing the difference between the value of a vulnerable portfolio and that of a riskfree one with identical characteristics. We propose a dynamic programming valuation method, where the value of the adjustment depends on the composition of the portfolio, the observed value of the underlying asset(s) and/or of the risk factors, and on the time to maturity. We present numerical illustrations and discuss the numerical challenges presented by netting agreements