Showing papers in "Mathematics and Financial Economics in 2022"
TL;DR: In this paper , a Principal-Agent model is proposed for the French government's green bond market, in which an investor trades on a portfolio of green and conventional bonds, both issued by the same governmental entity, and the government provides incentives to the bondholder in order to increase the amount invested in green bonds.
Abstract: Motivated by the recent studies on the green bond market, we build a Principal–Agent model in which an investor trades on a portfolio of green and conventional bonds, both issued by the same governmental entity. The government provides incentives to the bondholder in order to increase the amount invested in green bonds. These incentives are, optimally, indexed on the prices of the bonds, their quadratic variation and covariation. We show numerically on a set of French governmental bonds that our methodology outperforms the current tax-incentives systems in terms of green investments. Moreover, it is robust to model specification for bond prices and can be applied to a large portfolio of bonds using classical optimisation methods.
7 citations
TL;DR: In this article , the authors propose a model for the debt-to-GDP (Gross Domestic Product) ratio where the government interventions via fiscal policies affect the public debt and the GDP growth rate at the same time, and prove that the value function is a viscosity solution to the Hamilton-Jacobi-Bellman equation.
Abstract: We discuss a class of debt management problems in a stochastic environment model. We propose a model for the debt-to-GDP (Gross Domestic Product) ratio where the government interventions via fiscal policies affect the public debt and the GDP growth rate at the same time. We allow for stochastic interest rate and possible correlation with the GDP growth rate through the dependence of both the processes (interest rate and GDP growth rate) on a stochastic factor which may represent any relevant macroeconomic variable, such as the state of economy. We tackle the problem of a government whose goal is to determine the fiscal policy in order to minimize a general functional cost. We prove that the value function is a viscosity solution to the Hamilton-Jacobi-Bellman equation and provide a Verification Theorem based on classical solutions. We investigate the form of the candidate optimal fiscal policy in many cases of interest, providing interesting policy insights. Finally, we discuss two applications to the debt reduction problem and debt smoothing, providing explicit expressions of the value function and the optimal policy in some special cases.
2 citations
2 citations
TL;DR: In this article , the authors study the competition of two strategic agents for liquidity in the benchmark portfolio tracking setup of Bank et al. and reveal how the equilibrium strategies of the two players take into account the other agent's trading targets: either in an exploitative intent or by providing liquidity to the competitor.
Abstract: Abstract We study the competition of two strategic agents for liquidity in the benchmark portfolio tracking setup of Bank et al. (Math Financial Economics 11(2):215–239 2017). Specifically, both agents track their own stochastic running trading targets while interacting through common aggregated temporary and permanent price impact à la Almgren and Chriss (J Risk 3:5–39 2001). The resulting stochastic linear quadratic differential game with terminal state constraints allows for a unique and explicitly available open-loop Nash equilibrium. Our results reveal how the equilibrium strategies of the two players take into account the other agent’s trading targets: either in an exploitative intent or by providing liquidity to the competitor, depending on the relation between temporary and permanent price impact. As a consequence, different behavioral patterns can emerge as optimal in equilibrium. These insights complement and extend existing studies in the literature on predatory trading models examined in the context of optimal portfolio liquidation games.
2 citations
2 citations
2 citations
TL;DR: In this article , the authors study mean field portfolio games with consumption and establish a one-to-one correspondence between Nash equilibria of the game and solutions to some FBSDE, which is proved to be equivalent to some BSDE.
Abstract: We study mean field portfolio games with consumption. For general market parameters, we establish a one-to-one correspondence between Nash equilibria of the game and solutions to some FBSDE, which is proved to be equivalent to some BSDE. Our approach, which is general enough to cover power, exponential and log utilities, relies on martingale optimality principle in Cheridito and Hu (Stochast Dyn 11(02n03):283–299, 2011) and Hu et al. (Ann Appl Probab 15(3):1691–1712, 2005) and dynamic programming principle in Espinosa and Touzi (Math Financ 25(2):221–257, 2015) and Frei and dos Reis (Math Financ Econ 4:161–182, 2011). When the market parameters do not depend on the Brownian paths, we get the unique Nash equilibrium in closed form. As a byproduct, when all market parameters are time-independent, we answer the question proposed in Lacker and Soret (Math Financ Econ 14(2):263–281, 2020): the strong equilibrium obtained in Lacker and Soret (Math Financ Econ 14(2):263–281, 2020) is unique in the essentially bounded space.
2 citations
TL;DR: In this article , the authors study a consumption-investment decision problem related to the past spending maximum and derive semi-explicit forms of the value function, optimal consumption plan, and optimal investment strategy.
Abstract: We study a consumption-investment decision problem related to the past spending maximum. In the problem, we consider two crucial consumption levels: the lowest constrained level and a reference level, and both levels are fractions of the past spending maximum. The decision-maker has different risk aversions on different sides of the reference level. We solve this stochastic control problem and derive semi-explicit forms of the value function, optimal consumption plan, and optimal investment strategy. We find five important wealth thresholds which are nonlinear functions of the past spending maximum. Based on numerical results and theoretical analysis, we also find that the model has significant economic implications. There are at least three important predictions: the marginal propensity to consume out of wealth is generally decreasing but can be increasing for intermediate wealth levels, and it varies inversely with risk aversion at the reference level; the implied relative risk aversion is roughly a smile in wealth; the welfare is much more vulnerable to wealth shocks when the reference level is not reached.
2 citations
TL;DR: In this article , the authors investigate a utility maximization problem with drift uncertainty in a multivariate continuous-time Black-Scholes type financial market which may be incomplete and show that the optimal strategy converges to a generalized uniform diversification strategy.
Abstract: Abstract In this paper we investigate a utility maximization problem with drift uncertainty in a multivariate continuous-time Black–Scholes type financial market which may be incomplete. We impose a constraint on the admissible strategies that prevents a pure bond investment and we include uncertainty by means of ellipsoidal uncertainty sets for the drift. Our main results consist firstly in finding an explicit representation of the optimal strategy and the worst-case parameter, secondly in proving a minimax theorem that connects our robust utility maximization problem with the corresponding dual problem. Thirdly, we show that, as the degree of model uncertainty increases, the optimal strategy converges to a generalized uniform diversification strategy.
1 citations
TL;DR: In this paper , the authors established general collapse to the mean (CTM) principles that provide conditions under which a law-invariant functional reduces to an expectation in the convex setting.
Abstract: Abstract We establish general “collapse to the mean” principles that provide conditions under which a law-invariant functional reduces to an expectation. In the convex setting, we retrieve and sharpen known results from the literature. However, our results also apply beyond the convex setting. We illustrate this by providing a complete account of the “collapse to the mean” for quasiconvex functionals. In the special cases of consistent risk measures and Choquet integrals, we can even dispense with quasiconvexity. In addition, we relate the “collapse to the mean” to the study of solutions of a broad class of optimisation problems with law-invariant objectives that appear in mathematical finance, insurance, and economics. We show that the corresponding quantile formulations studied in the literature are sometimes illegitimate and require further analysis.
1 citations
TL;DR: In this paper , the authors consider a large population dynamic game in discrete time where players are characterized by time-evolving types and derive existence and uniqueness of equilibria under suitable assumptions, and study the convergence of the natural fixed-point iterations scheme in the quadratic case.
Abstract: Abstract We consider a large population dynamic game in discrete time where players are characterized by time-evolving types. It is a natural assumption that the players’ actions cannot anticipate future values of their types. Such games go under the name of dynamic Cournot-Nash equilibria , and were first studied by Acciaio et al. (SIAM J Control Optim 59:2273–2300, 2021), as a time/information dependent version of the games devised by Blanchet and Carlier ( Math Oper Res 41:125–145, 2016) for the static situation, under an extra assumption that the game is of potential type. The latter means that the game can be reduced to the resolution of an auxiliary variational problem. In the present work we study dynamic Cournot-Nash equilibria in their natural generality, namely going beyond the potential case. As a first result, we derive existence and uniqueness of equilibria under suitable assumptions. Second, we study the convergence of the natural fixed-point iterations scheme in the quadratic case. Finally we illustrate the previously mentioned results in a toy model of optimal liquidation with price impact, which is a game of non-potential kind.
TL;DR: In this article , an equilibrium model of dynamic trading, learning, and pricing by strategic investors with trading targets and price impact is presented, where trading targets are private and investors filter the child order flow dynamically over time to estimate the latent underlying parent trading demand imbalance and to forecast its impact on subsequent price pressure dynamics.
Abstract: Abstract We present an equilibrium model of dynamic trading, learning, and pricing by strategic investors with trading targets and price impact. Since trading targets are private, investors filter the child order flow dynamically over time to estimate the latent underlying parent trading demand imbalance and to forecast its impact on subsequent price-pressure dynamics. We prove existence of an equilibrium and solve for equilibrium trading strategies and prices as the solution to a system of coupled ODEs. Trading strategies are combinations of trading towards investor targets, liquidity provision for other investors’ demands, and speculation based on learning about latent underlying trading-demand imbalances.
TL;DR: In a continuous-time market with a safe rate and a risky asset that pays a dividend stream depending on a latent state of the economy, several agents make consumption and investment decisions based on public information-prices and dividends-and private signals as discussed by the authors .
Abstract: In a continuous-time market with a safe rate and a risky asset that pays a dividend stream depending on a latent state of the economy, several agents make consumption and investment decisions based on public information-prices and dividends-and private signals. If each investor has constant absolute risk aversion, equilibrium prices do not reveal all the private signals, but lead to the same estimate of the state of the economy that one would hypothetically obtain from the knowledge of all private signals. Accurate information leads to low volatility, ostensibly improving market efficiency, but also reduces each agent's consumption through a decrease in the price of risk. Thus, informational efficiency is reached at the expense of agents' welfare.
TL;DR: This article proposed a Cournot-type equilibrium model where firms choose mitigation efforts and production quantities such as to maximize the expected profits under their subjective beliefs, and showed that optimal mitigation efforts are increased by the presence of uncertainty and act as substitutes; i.e., one firm's lack of mitigation incentivizes others to act more decidedly and vice versa.
Abstract: We study strategic interactions between firms with heterogeneous beliefs about future climate impacts. To that end, we propose a Cournot-type equilibrium model where firms choose mitigation efforts and production quantities such as to maximize the expected profits under their subjective beliefs. It is shown that optimal mitigation efforts are increased by the presence of uncertainty and act as substitutes; i.e., one firm’s lack of mitigation incentivizes others to act more decidedly, and vice versa.
TL;DR: In this paper , a class of multivariate tempered stable distributions and associated class of tempered stable Sato subordinators are used to build additive inhomogeneous processes by subordination of a multiparameter Brownian motion.
Abstract: Abstract We study a class of multivariate tempered stable distributions and introduce the associated class of tempered stable Sato subordinators. These Sato subordinators are used to build additive inhomogeneous processes by subordination of a multiparameter Brownian motion. The resulting process is additive and time inhomogeneous and it is a generalization of multivariate Lévy processes with good fit properties on financial data. We specify the model to have unit time normal inverse Gaussian distribution and we discuss the ability of the model to fit time inhomogeneous correlations on real data.