Portfolio optimization for a large investor under partial information and price impact

This paper studies portfolio optimization problems in a market with partial information and price impact. We consider a large investor with an objective of expected utility maximization from terminal wealth. The drift of the underlying price process is modeled as a diffusion affected by a continuous-time Markov chain and the actions of the large investor. Using the stochastic filtering theory, we reduce the optimal control problem under partial information to the one with complete observation. For logarithmic and power utility cases we solve the utility maximization problem explicitly and we obtain optimal investment strategies in the feedback form. We compare the value functions to those for the case without price impact in Bäuerle and Rieder (IEEE Trans Autom Control 49(3):442–447, 2004) and Bäuerle and Rieder (J Appl Prob 362–378, 2005). It turns out that the investor would be better off due to the presence of a price impact both in complete-information and partial-information settings. Moreover, the presence of the price impact results in a shift, which depends on the distance to final time and on the state of the filter, on the optimal control strategy.     

Optimal portfolio for a small investor in a market model with discontinuous prices

A consumption-investment problem is considered for a small investor in the case of a market model in which prices evolve according to a stochastic equation with a jump-process component. The techniques we use include the martingale representation theorem, Lagrange multiplier methods, and Markovian methods for the resolution of stochastic differential equations. We establish a Black-Scholes formula.     

双指数跳扩散模型的美式二值期权定价

在股价满足红利连续支付的双指数跳扩散模型下,研究美式二值现金-无值看涨期权的定价问题.通过分解方法将其定价转化成求一个对应的永久美式期权价格和一个Cauchy问题的解,从而得到定价表达式.最后给出一个计算实例.     

A class of exact solutions for a kinetic model of an equilibrium plasma

The stationary Vlasov-Maxwell system is reduced to a resolving equation of sinh-Gordon type. It is shown that for fully ionized hydrogen and helium plasmas the resolving equation will have the form of the sinh-Gordon equation and Bullough-Dodd-Zhiber-Shabat equation (with elliptic operator), respectively. Hirota's method is used to obtain exact solutions for these equations. From these solutions, the characteristics of the system are recovered: the distribution functions and the self-consistent electromagnetic field.Irkutsk Computational Center, Siberian Branch, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 91, No. 1, pp. 129–141, April, 1992.     

A linear production-exchange model: Polyhedral complexes and a criterion for an equilibrium

Under study is an economic model of exchange whose participants include consumers as well as companies producing commodities. The production capabilities of the companies are constrained by the expenses of a certain single resource. We scrutinize the version of the model with fixed budgets of the participants, show that some equilibrium exists, and describe an original approach of polyhedral complementarity which enables us to obtain a criterion for an equilibrium state. Thus, we can propose a finite algorithm for finding an equilibrium.     

Weak equilibrium in a spatial model

Spatial models of two-player competition in spaces with more than one dimension almost never have pure-strategy Nash equilibria, and the study of the equilibrium positions, if they exist, yields a disappointing result: the two players must choose the same position to achieve equilibrium. In this work, a discrete game is proposed in which the existence of Nash equilibria is studied using a geometric argument. This includes a definition of equilibrium which is weaker than the classical one to avoid the uniqueness of the equilibrium position. As a result, a “region of equilibrium” appears, which can be located by geometric methods. In this area, the players can move around in an “almost-equilibrium” situation and do not necessarily have to adopt the same position.     

An equilibrium model for urban transit assignment based on game theory

The urban public transport system is portrayed as a special commodity market where passenger is consumer, transit operator is producer and the special goods is the service for passenger’s trip. The generalized Nash equilibrium game is applied to describe how passengers adjust their route choices and trip modes. We present a market equilibrium model for urban public transport system as a series of mathematical programmings and equations, which is to describe both the competitions among different transit operators and the interactive influences among passengers. The proposed model can simultaneously predict how passengers choose their optimal routes and trip modes. An algorithm is designed to obtain the equilibrium solution. Finally, a simple numerical example is given and some conclusions are drawn.     

Solving an equilibrium model for trade of CO2 emission permits

In this paper we investigate the trade of CO₂ emission permits in the framework of a competitive economic equilibrium. For this purpose we integrate already existing regional energy-economy models (Markal-Macro) into a single multi-regional trade model. Based on two possible integration schemes we discuss two solution concepts: the first is based on pseudomonotonicity of the excess map whereas the second is a fixed point approach due to Negishi. In the latter case the overall optimization problem is decomposed. For both algorithms the regional subproblems were distributed on different computers and solved in parallel. We conclude by presenting numerical results of a model with full data sets for Switzerland, Sweden and the Netherlands.     

An oracle based method to compute a coupled equilibrium in a model of international climate policy

This paper proposes a computational game-theoretic model for the international negotiations that should take place at the end of the period covered by the Kyoto protocol. These negotiations could lead to a self-enforcing agreement on a burden sharing scheme given the necessary global emissions limit that will be imposed when the real extent of climate change is known. The model assumes a non-cooperative behavior of the parties except for the fact that they will be collectively committed to reach a target on total cumulative emissions by the year 2050. The concept of normalized equilibrium, introduced by J.B. Rosen for concave games with coupled constraints, is used to characterize a family of dynamic equilibrium solutions in an m-player game where the agents are (groups of) countries and the payoffs are the welfare gains obtained from a Computable General Equilibrium (CGE) model. The model deals with the uncertainty about climate sensitivity by computing an S-adapted equilibrium. These equilibria are computed using an oracle-based method permitting an implicit definition of the payoffs to the different players, obtained through simulations performed with the global CGE model GEMINI-E3. Partly supported by GICC (French Ministry of Ecology), TOCSIN (EU-044287) and the Swiss-NSF NCCR-Climate program of the Swiss NSF. For helpful comments and discussions, we thank A. Bernard, P. Thalmann, and the anonymous referee.     

Approximating the optimum portfolio for an investor with particular preferences

The optimum portfolio for an investor who has a well-defined particular preference for profitability and safety is approximated on the mean-variance efficient frontier by resorting to a new bounding utility theorem which is stated and proven in the paper.     

Chaos in a dynamic model of urban transportation network flow based on user equilibrium states

In this study, we investigate the dynamical behavior of network traffic flow. We first build a two-stage mathematical model to analyze the complex behavior of network flow, a dynamical model, which is based on the dynamical gravity model proposed by Dendrinos and Sonis [Dendrinos DS, Sonis M. Chaos and social-spatial dynamic. Berlin: Springer-Verlag; 1990] is used to estimate the number of trips. Considering the fact that the Origin–Destination (O–D) trip cost in the traffic network is hard to express as a functional form, in the second stage, the user equilibrium network assignment model was used to estimate the trip cost, which is the minimum cost of used path when user equilibrium (UE) conditions are satisfied. It is important to use UE to estimate the O–D cost, since a connection is built among link flow, path flow, and O–D flow. The dynamical model describes the variations of O–D flows over discrete time periods, such as each day and each week. It is shown that even in a system with dimensions equal to two, chaos phenomenon still exists. A “Chaos Propagation” phenomenon is found in the given model.     

Law of large numbers in an epidemic model

Doklady Mathematics -     

Investigations on an elastic micropolar continuum model for large deformations

The mechanical behaviour of cellular materials is dominated by the influence of the microtopology. If the characteristic microstructural length scale becomes comparable to the macroscopical length scale, classical homogenisation strategies fail and have to be replaced by extended approaches. In the present contribution, we present a micropolar continuum model for large deformations introducing the microrotation as an additional degree of freedom. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Forward–backward SDEs with random terminal time and applications to pricing special European-type options for a large investor

In this paper, we first discuss the solvability of coupled forward–backward stochastic differential equations (FBSDEs, for short) with random terminal time. We prove the existence and uniqueness of adapted solution to such FBSDEs under some natural assumptions. The method of proof adopted is to construct a contraction mapping related to the solutions of a sequence of backward SDEs. Our monotonicity-type assumptions are different from those in Hu and Peng (1995) [4], Peng and Shi (2000) [11], and so on. As a corollary of our main result, the solvability of FBSDEs with a finite time horizon is discussed. Finally, the existence and uniqueness theorem of the solution to FBSDEs with a finite time horizon is applied to price special European-type options for a large investor.     

Edgeworth equilibrium in a model of interregional economic relations

We introduce an analog of an Edgeworth equilibrium for a class of multiregional economic systems. We analyze the game-theoretic aspects of the coalition stability of regional development plans and establish a quite general existence theorem for an Edgeworth equilibrium. We discuss the questions of coincidence of the set of these equilibria with the fuzzy core and the set of theWalrasian equilibria of the multiregional systemin question.Our methods rest on a systematic accounting for the polyhedrality of the sets of balanced coalition plans.     

Pricing and lot sizing for an EPQ inventory model with rework and multiple shipments

This paper deals with an economic production quantity (EPQ) inventory model with reworkable defective items when a given multi-shipment policy is used. In this work, it is assumed that in each cycle, the rework process of all defective items starts when the regular production process finishes. After the rework process, a portion of reworked items fails. This portion becomes scrap and only the perfect finished items can be delivered to customers at the end of rework process. A profit function is derived to model the inventory problem and it is shown that the profit function is concave. Due to the complexity of the optimization problem, an algorithm is developed to determine the optimal values of manufacturing lot size and price such that the long-run average profit function is maximized. Furthermore, two special cases are identified and explained. Finally, a numerical example is given to illustrate the applicability of the proposed inventory model.     

Pricing annuity guarantees under a double regime-switching model

This paper is concerned with the valuation of equity-linked annuities with mortality risk under a double regime-switching model, which provides a way to endogenously determine the regime-switching risk. The model parameters and the reference investment fund price level are modulated by a continuous-time, finite-time, observable Markov chain. In particular, the risk-free interest rate, the appreciation rate, the volatility and the martingale describing the jump component of the reference investment fund are related to the modulating Markov chain. Two approaches, namely, the regime-switching Esscher transform and the minimal martingale measure, are used to select pricing kernels for the fair valuation. Analytical pricing formulas for the embedded options underlying these products are derived using the inverse Fourier transform. The fast Fourier transform approach is then used to numerically evaluate the embedded options. Numerical examples are provided to illustrate our approach.