4th NUS-USPC Workshop
11 – 12 Apr 2017, Singapore
PROGRAMME ABSTRACTS| Tuesday, 11 April 2017 | |
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Time |
Activity |
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08:50 – 09:10 |
Registration |
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09:10 – 09:20 |
Opening Address |
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09:20 – 10:00 |
Masaaki KIJIMA Tokyo Metropolitan University, Japan Solution to The Time-Scale Fractional Puzzle in The Implied Volatility with Rough Market Price of Volatility Risk |
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10:00 – 10:40 |
Bin LI University of Waterloo, Canada Alpha-Maxmin Utility Maximization: An Equilibrium Approach |
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10:40 – 11:00 |
Group Photo cum Tea Break |
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11:00 – 11:40 |
Hanqing JIN University of Oxford, United Kingdom Time Inconsistent Utility Maximisation with Regime-Dependent Risk Aversion |
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11:40 – 12:10 |
Cyril BENEZET University Paris Diderot, France Approximate Hedging Problems: Numerical Methods |
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12:10 – 13:20 |
Lunch |
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13:20 – 14:00 |
Jean-François CHASSAGNEUX University Paris Diderot, France New results on obliquely reflected BSDEs |
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14:00 – 14:40 |
Noufel FRIKHA University Paris Diderot, France Hitting Times of on Dimensional Elliptic Diffusions and Monte Carlo Approximation |
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14:40 – 15:10 |
Wei JIANG National University of Singapore, Singapore Simulating Risk Measures |
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15:10 – 15:30 |
Break |
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15:30:- 16:00 |
Cong QIN National University of Singapore, Singapore Exhaustible Resources with Exploration and Production Adjustment Costs |
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16:00 – 16:30 |
Xiaoli WEI University Paris Diderot, France A Dynamic Programming Approach for Discrete Time Mckean-Vlasov Control Problem |
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16:30 – 17:00 |
Matteo BASEI University Paris Diderot, France The Coordination of Centralised and Distributed Generation |
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Wednesday, 12 April 2017 | |
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Time |
Activity |
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09:00 – 09:20 |
Registration |
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09:20 – 10:00 |
Youri KABANOV University of Franche-Comté, France Arbitrage Theory under Transaction Costs |
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10:00 – 10:40 |
Xiang YU Hong Kong Polytechnic University, Hong Kong On the Market Viability under Proportional Transaction Costs |
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10:40 – 11:00 |
Tea Break |
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11:00 – 11:40 |
Huyên PHAM University Paris Diderot, France Robust Markowitz Portfolio Selection under Ambiguous Volatility and Correlation |
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11:40 – 12:10 |
Shan HUANG National University of Singapore, Singapore Life-Cycle Consumption, Investment, and Voluntary Retirement with Cointegration between the Stock and Labor Markets |
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12:10 – 13:20 |
Lunch |
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13:20 – 14:00 |
Claudio FONTANA University Paris Diderot, France Affine Multiple Yield Curve Models |
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14:00 – 14:40 |
Simone SCOTTI University Paris Diderot, France Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling |
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14:40 – 14:50 |
Closing Address |
Abstracts
The Coordination of Centralised and Distributed Generation Matteo BASEI, University Paris Diderot, France We analyse the interaction between centralised carbon emissive technologies and distributed intermittent non-emissive technologies. In our model, there is a representative consumer who can satisfy her electricity demand by investing in distributed generation (solar panels) and by buying power to a centralised firm at a price he set up. Distributed generation is intermittent and induces an externality cost to the consumer. The firm provides non-random electricity generation subject to carbon price and to transmission costs. The objective of the consumer is to satisfy her demand while minimising investment costs, payment to the firm and intermittency cost. The objective of the firm is to satisfy consumer’s residual demand while minimising investment costs, demand deviation costs and maximising payment from the consumer. Investment decisions are formulated as McKean-Vlasov control problems with stochastic coefficients. We provide explicit, model-free solutions to the optimal decision problems faced by each player, the solution of the Pareto optimum and the Stackelberg equilibrium where the firm is the leader. We find that, from the social planner point of view, carbon price or transmission costs are necessary to justify a positive share of distributed capacity in the long-term, whatever the respective investment costs of both technologies are. The Stackelberg equilibrium is far from the Pareto equilibrium, leading to a much larger share of distributed energy and to a much higher price for centralised energy. This is a joint work with René AID (University Paris Dauphine, France), Imen BEN TAHAR (University Paris Dauphine, France) and Huyên PHAM (University Paris Diderot, France).Approximate Hedging Problems: Numerical Methods Cyril BENEZET, University Paris Diderot, France In this talk, we are going to introduce the problem of approximate hedging. For example, for long-term insurance products, surreplication price is often too high to be used; pricing and hedging under controlled loss is then required. After recalling the stochastic problem modeling this issue and the PDE that the value function solves (in the viscosity sense), we discuss numerical issues and strategies to overcome those difficulties. This is a joint work with Jean-François Chassagneux (University Paris Diderot, France).
New results on obliquely reflected BSDEs Jean-François CHASSAGNEUX, University Paris Diderot, France I will present new existence and uniqueness results obtained for BSDEs that are reflected in a convex domain. The direction of reflection is allowed to be oblique with respect to the normal reflection. The motivation comes from various stochastic control problems that I will discuss as well.
Affine Multiple Yield Curve Models Claudio FONTANA, University Paris Diderot, France We provide a general and tractable framework under which all multiple yield curve modeling approaches based on affine processes, be it short rate, Libor market, or Heath-Jarrow-Morton modeling, can be consolidated. We model a numeraire process and multiplicative spreads between Libor rates and simply compounded OIS rates as functions of an underlying affine process. Besides allowing for ordered spreads and an exact fit to the initially observed term structures, this general framework leads to tractable valuation formulas for caplets and swaptions and embeds all existing multi-curve affine models. The proposed approach also gives rise to new developments, such as a short rate type model driven by a Wishart process, for which we derive a closed-form pricing formula for caplets. The empirical performance of two specifications of our framework is illustrated by calibration to market data. This is based on joint work with Christa CUCHIERO (University of Vienna, Austria) and Alessandro GNOATTO (BayernLB, Germany).
Hitting Times of on Dimensional Elliptic Diffusions and Monte Carlo Approximation Noufel FRIKHA, University Paris Diderot, France During this presentation, we investigate some properties of the law associated to the first hitting time of a threshold by a one-dimensional uniformly elliptic diffusion process and the associated process stopped at the threshold. Our methodology relies on a perturbation method, known as the parametrix, that we apply to the associated Markov semigroup. This method allows to obtain explicit expressions for the corresponding transition densities and to study its regularity properties up to the boundary under mild assumptions on the coefficients. As a by product, we also provide a probabilistic representation that may be useful for the construction of an unbiased Monte Carlo path simulation method, among other applications. This is a joint work with Arturo KOHATSU-HIGA (Ristumeikan University, Japan) and Libo LI (University of New South Wales, Australia).
Life-Cycle Consumption, Investment, and Voluntary Retirement with Cointegration between the Stock and Labor Markets Shan HUANG, National University of Singapore, Singapore We present an optimal life-cycle consumption, investment, and voluntary retirement model for a borrowing and short sale constrained investor who faces cointegration between the stock and labor markets. With reasonable parameter values, there exists a target wealth-to-income ratio under which the investor does not participate in the stock market at all, whereas above which the investor increases the proportion of financial wealth invested in the stock market as she accumulates wealth. We analyze the effects on investment of retirement flexibility with and without cointegration. We also isolate the effects on retirement of risk aversion with and without uninsurable income risks. The model presented here predicts that early retirement is economically plausible in the stock market booms, like those observed in the late 1990’s. This is a joint work with Min DAI (National University of Singapore, Singapore) and Seyoung PARK (National University of Singapore, Singapore).
Simulating Risk Measures Wei JIANG, National University of Singapore, Singapore Risk measures, such as value-at-risk and expected shortfall, are widely used in risk management, as exemplified in the Basel Accords proposed by Bank of International Settlements. We propose a simple general framework, allowing dependent samples, to compute these risk measures via simulation. The framework consists of two steps: in the S-step, risk measure is estimated by using selected sorting algorithm; in R-step, necessary sample size is computed based on newly derived asymptotic expansions of relative error for dependent samples, and the S-step is repeated until requirement on relative error is met. We systematically investigate various sorting methods in the S-step. Numerical experiments indicate that the algorithm is easy to implement and fast, compared to existing methods, even at the 0.001 quantile level. We also give a comparison of the relative errors of value-at-risk and expected shortfall. This is a joint work with Steven KOU (National University of Singapore, Singapore).
Time Inconsistent Utility Maximisation with Regime-Dependent Risk Aversion Hanqing JIN, University of Oxford, United Kingdom We study the utility maximisation problem in a continuous time market with regime switching. The regime does not only enter into the market parameters, but also changes the preference modelled by utility function. With the changing utility function, the utility maximisation problem is not time consistent. In this paper, we aims at the equilibrium trading strategy defined for time-inconsistent dynamic decision problem. We find out explicit equilibrium trading strategies for two types of utility functions. Surprisingly, they happen to be the same as the naive trading strategies, which are relatively easy to find but lack of justification in general.
Arbitrage Theory under Transaction Costs Youri KABANOV, University of Franche-Comté, France The cornerstone of classical arbitrage theory of frictionless financial markets is the Dalang-Morton-Willinger theorem which relates financially important notion of absence of arbitrage with fundamental concepts of theory of random processes. Its modern formulation says that the absence of arbitrage is equivalent to the existence of a martingale deflator, i.e. a multiplicator converting nominal prices into prices having a specific consistency property, namely, the martingale one. It will be presented an elementary model of financial market with proportional transaction costs which analysis is based on geometric considerations. The theory is different from the classical one in many aspects. In particular, for markets with friction consistent price systems are formed by martingales evolving in a dual to the solvency cones in physical units. Several surprising results will be discussed.
Solution to The Time-Scale Fractional Puzzle in The Implied Volatility with Rough Market Price of Volatility Risk Masaaki KIJIMA, Tokyo Metropolitan University, Japan There is a general consensus that the volatility displays long-memory. Comte and Renault (1998) show that, thanks to this feature, the decrease of volatility smile amplitude with respect to time to maturity of fractional volatility model with Hurst index greater than 0.5 is slower than that of traditional stochastic volatility models. On the other hand, inconsistent with this fact, Gatheral et al. (2014) find the evidence of rough volatility from high frequency data and show that the log-volatility behaves as a fractional Brownian motion with Hurst index of order 0.1 when time to maturity is short. The aim of this paper is to provide a solution to this time-scale fractional puzzle in the implied volatility. To this end, we extend the model proposed by Funahashi and Kijima (2017) so as to incorporate the fractional market price of volatility risk with Hurst index of order 0.1. Herewith, both the long memory feature under the physical measure and the volatility roughness under the risk-neutral measure can be explained simultaneously, just like the grand unification theory in physics. It is demonstrated through numerical experiments that our model can explain both the slower decay of the smile amplitude decrease and the term structure of the at-the-money volatility skew observed in the implied volatility. This is a joint work with Hideharu FUNAHASHI (Mizuho Securities Co. Ltd, Japan).
Alpha-Maxmin Utility Maximization: An Equilibrium Approach Bin LI, University of Waterloo, Canada The existing literature of utility maximization with ambiguity usually assumes the decision maker is extremely ambiguity averse. However, there is few behavioral experiment to support such extreme pessimistic ambiguity attitude. In light of complex attitudes towards ambiguity, the so-called α-maxmin utility was proposed and has been studied extensively in the economics literature. There is surprisingly little study on the benchmark maximization problem for the α-maxmin utility, and the main difficulty comes from two parts: non-concavity and dynamic inconsistency. In this paper, we adopt an equilibrium approach to formulate the problem into a non-cooperative game and look for a Nash equilibrium. Under a general Markovian financial market model, we show that the existence of equilibrium strategies can be reduced to the study of a fully coupled quadratic BSDE system. The existence and uniqueness to the BSDE system are proved by utilizing some recent development in this area.
Robust Markowitz Portfolio Selection under Ambiguous Volatility and Correlation Huyên PHAM, University Paris Diderot, France This talk addresses a robust continuous-time Markowitz portfolio selection problem where the model uncertainty carries on the variance-covariance matrix of the risky assets. This problem is formulated into a min-max mean-variance problem over a set of non-dominated probability measures that is solved by a McKean-Vlasov dynamic programming approach, which allows us to characterize the solution in terms of a Bellman-Isaacs equation in the Wasserstein space of probability measures. We provide explicit solutions for the optimal robust portfolio strategies in the case of uncertain volatilities and ambiguous correlation between two risky assets, and then derive the robust efficient frontier in closed-form. We obtain a lower bound for the Sharpe ratio of any robust efficient portfolio strategy, and compare the performance of Sharpe ratios for a robust investor and for an investor with a misspecified model.
Exhaustible Resources with Exploration and Production Adjustment Costs Cong QIN, National University of Singapore, Singapore In this paper, we develop a general equilibrium model of exhaustible resources with production adjustment costs by singular control. There exists a unique socially optimal consumption path which consists of a no-adjustment part and can be reproduced by a competitive market. Based on the basic model, we further give an extension to incorporate demand uncertainty and exploration activity. In particular, uncertainties combined with adjustment costs can naturally explain many economic phenomena observed in the real markets, such as backwardation, contango, Samuelson effect, and high volatility conditional on backwardation. Finally, compared to either using exploration or production adjustments only, the combination of both exploration and production adjustments can significantly prolong the price staying at the bottom. This may help us to understand why prices of many commodities can be quite low for a long time.
Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling Simone SCOTTI, University Paris Diderot, France We introduce a class of interest rate models, called the α-CIR model, which gives a natural extension of the standard CIR model by adopting the α-stable L{\’e}vy process and preserving the branching property. This model allows to describe in a unified and parsimonious way several recent observations on the sovereign bond market such as the persistency of low interest rate together with the presence of large jumps at local extent. We emphasize on a general integral representation of the model by using random fields, with which we establish the link to the CBI processes and the affine models. Finally we analyze the jump behaviors and in particular the large jumps, and we provide numerical illustrations. This is a joint work with Ying JIAO (ISFA Lyon, France) and Chunhua MA (Nankai University, China).
A Dynamic Programming Approach for Discrete Time Mckean-Vlasov Control Problem Xiaoli WEI, University Paris Diderot, France We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distributions as controlled state variable and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance problem and the multivariate linear-quadratic Mckean-Vlasov control problem. This is a joint work with Huyên PHAM (University Paris Diderot, France).
On the Market Viability under Proportional Transaction Costs Xiang YU, Hong Kong Polytechnic University, Hong Kong This project studies the market viability with proportional transaction costs. Instead of requiring the existence of strictly consistent price systems (SCPS) as in the literature, we show that strictly consistent local martingale systems (SCLMS) can successfully serve as the dual elements such that the market viability can be verified. We introduce two weaker notions of no arbitrage conditions on market models named no unbounded profit with bounded risk (NUPBR) and no local arbitrage with bounded portfolios (NLABP). In particular, we show that the NUPBR and NLABP conditions in the robust sense are equivalent to the existence of SCLMS for general market models. We also discuss the implications for the utility maximization problem. This is the joint work with Erhan BAYRAKTAR (University of Michigan).