Two-agent Pareto optimal cooperative investment in general semimartingale model

We consider the problem of expected utility maximization for the two-agent case in general semimartingale model. For this case a cooperative investment game is posed as follows: firstly collect both agents' capital as a whole at the initial time, and invest it in a trading strategy. Then at some time T ₀ one agent quits cooperation and terminates investment, so they divide the wealth and each of them gets a part. During the time interval [T ₀, T], the other agent invests her capital in a new trading strategy herself. By stochastic optimization methods with the help of the theory of backward stochastic differential equations, we give a characterization of Pareto optimal cooperative strategies and a characterization of situations where cooperation strictly Pareto dominates non-cooperation in our model.     

A cooperative game of information trading: The core,the nucleolus and the kernel

A certain trade of the information about a technological innovation between the initial owner of the information andn identical producers is studied by means of a cooperative game theoretic approach. The information trading situation is modelled as a cooperative (n+1)-person game with side payments. The symmetrical strong -cores (including the core), the nucleolus and the kernel of the cooperative game model are determined. Interpretations of these game theoretic solutions and their implications for the information trading problem are given.     

Risk minimizing hedging for a partially observed high frequency data model

Risk-minimizing hedging strategies for contingent claims are studied in a general model for intraday stock price movements in the case of partial information. The dynamics of the risky asset price is described throught a marked point process Y, whose local characteristics depend on some unobservable hidden state variable X. In the model presented the processes Y and X may have common jump times, which means that the trading activity may affect the law of X and could be also related to the presence of catastrophic events. The hedger is restricted to observing past asset prices. Thus, we are in presence not only of an incomplete market situation but also of partial information. Considering the case where the price of the risky asset is modeled directly under a martingale measure, the computation of the risk-minimizing hedging strategy under this partial information is obtained by using a projection result (M. Schweizer, Risk minimizing hedging strategies under restricted information, Mathematical Finance 4 (1994) 327–342). This approach leads to a filtering problem with marked point process observations whose solution, obtained via the Kushner-Stratonovich equation, allows us to provide a complete solution to the heding problem.     

Cooperative hedging with a higher interest rate for borrowing

The paper studies the cooperative hedging problem of contingent claims in an incomplete financial market. Firstly we give the characterization of the optimal cooperative hedging strategy for the Black-Scholes model and the Volatility Jump model explicitly, then we consider the problem of cooperative hedging for the multi-agent case in a market with a higher borrowing interest rate. By the results of concave and linear backward stochastic differential equations, we give the optimal cooperative hedging strategy in our model.     

Computing strategies for achieving acceptability: A Monte Carlo approach

We consider a trader who wants to direct his or her portfolio towards a set of acceptable wealths given by a convex risk measure. We propose a Monte Carlo algorithm, whose inputs are the joint law of stock prices and the convex risk measure, and whose outputs are the numerical values of initial capital requirement and the functional form of a trading strategy for achieving acceptability. We also prove optimality of the capital obtained. Explicit theoretical evaluations of hedging strategies are extremely difficult, and we avoid the problem by resorting to such computational methods. The main idea is to utilize the finite Vapnik–C?ervonenkis dimension of a class of possible strategies.     

Cooperative hedging in the complete market under <Emphasis Type="Italic">g</Emphasis>-expectation constraint

The paper studies the muiti-agent cooperative hedging problem of contingent claims in the complete market when the g-expected shortfall risks are bounded. We give the optimal cooperative hedging strategy explicitly by the Neyman-Pearson lemma under g-probability.     

Mean-variance Hedging for Pricing European-type Contingent Claims with Transaction Costs

In this paper,a European-type contingent claim pricing problem with transaction costs is considered by a mean-variance hedging argument.The investor has to pay transaction costs which areproportional to the amount of stock transacted.The writer‘‘s hedging object is to minimize the hedgingrisk,defined as the variance of hedging error at expiration,with a proper expected excess return level.At first, we consider the mean-variance hedging problem:for initial hedging wealth f,maximizing the excess expected return under the minimum hedging risk level V0.On the other hand,we consider a mean-variance portfolio problem,which is to maximize the expected return with initial wealth 0 under the same risk level V0.The minimum initial hedging wealth f,which can offset the difference of the maximum expected return of these two problems,is the writer‘s price.     

Some results on quadratic hedging with insider trading

We consider the hedging problem in an arbitrage-free incomplete financial market, where there are two kinds of investors with different levels of information about the future price evolution, described by two filtrations F and G=F∨σ(G) where G is a given r.v. representing the additional information. We focus on two types of quadratic approaches to hedge a given square-integrable contingent claim: local risk minimization (LRM) and mean-variance hedging (MVH). By using initial enlargement of filtrations techniques, we solve the hedging problem for both investors and compare their optimal strategies under both approaches.

In particular, for LRM, we show that for a large class of additional non trivial r.v.s G both investors will pursue the same locally risk minimizing portfolio strategy and the cost process of the ordinary agent is just the projection on F of that of the insider. For the MVH approach, we study also some general stochastic volatility model, including Hull and White, Heston and Stein and Stein models. In this more specific setting and for r.v.s G which are measurable with respect to the filtration generated by the volatility process, we obtain an expression for the insider optimal strategy in terms of the ordinary agent optimal strategy plus a process admitting a simple feedback-type representation.     

Efficient Hedging and Pricing of Life Insurance Policies in a Jump-Diffusion Model

Abstract

This paper is devoted to the problem of hedging contingent claims in the framework of a two factors jump-diffusion model under initial budget constraint. We give explicit formulas for the so called efficient hedging. These results are applied for the pricing of equity linked-life insurance contracts.     

L 2 -discrete hedging in a continuous-time model

In the setting of the Black-Scholes option pricing market model, the seller of a European option must trade continuously in time. This is, of course, unrealistic from the practical viewpoint. He must then follow a discrete trading strategy. However, it does not seem natural to hedge at deterministic times regardless of moves of the spot price. In this paper, it is supposed that the hedger trades at a fixed number N of rebalancing (stopping) times. The problem (P^N) of selecting the optimal hedging times and ratios which allow one to minimize the variance of replication error is considered. For given N rebalancing, the discrete optimal hedging strategy is identified for this criterion. The problem (P^N) is then transformed into a multidimensional optimal stopping problem with boundary constraints. The restrictive problem (P^N _BS) of selecting the optimal rebalancing for the same criterion is also considered when the ratios are given by Black-Scholes. Using the vector-valued optimal stopping theory, the existence is shown of an optimal sequence of rebalancing for each one of the problems (P^N) and (P^N _BS). It also shown BS that they are asymptotically equivalent when the number of rebalances becomes large and an optimality criterion is stated for the problem (P^N). The same study is made when more realistic restrictions are imposed on the hedging times. In the special case of two rebalances, the problem (P² _BS) is solved and the problems (P² _BS) and (P²) are transformed into two optimal stopping problems. This transformation is useful for numerical purposes.     

Risk Minimization for a Filtering Micromovement Model of Asset Price

Abstract

The classical option hedging problems have mostly been studied under continuous-time or equally spaced discrete-time models, which ignore two important components in the actual price: random trading times and market microstructure noise. In this paper, we study optimal hedging strategies for European derivatives based on a filtering micromovement model of asset prices with the two commonly ignored characteristics. We employ the local risk-minimization criterion to develop optimal hedging strategies under full information. Then, we project the hedging strategies on the observed information to obtain hedging strategies under partial information. Furthermore, we develop a related nonlinear filtering technique under the minimal martingale measure for the computation of such hedging strategies.     

乡村振兴战略下农村人居环境整治PPP模式合作行为演化博弈分析

农村人居环境整治是乡村振兴战略的重要内容,基于有限理性的演化博弈理论,构建了以地方政府、社会资本和农村居民为博弈主体的农村人居环境整治PPP模式合作行为演化博弈模型,运用Matlab软件分析了三方主体的初始意愿和政府规制对三方主体行为策略演化的影响。研究发现:(1)政府规制对农村人居环境整治PPP模式合作博弈系统演化的影响从大到小依次是:政府对社会资本的补贴资助、投机罚金、合作奖励和政府对农村居民的参与奖励。(2)与提高地方政府对社会资本的补贴资助力度和惩罚力度相比,提高地方政府的激励规制初始意愿更能促进农村人居环境整治PPP项目的顺利落地实施。(3)农村居民参与PPP项目的初始意愿的提升关键在于提高农村居民参与收益。最后,为促进PPP模式在农村环境治理领域的应用与发展和推动农村人居环境整治的可持续改善提出相应建议。     

基于供需网企业合作博弈模型的演化路径分析

传统企业间合作博弈问题的研究大都是基于合作策略和不合作策略两种情形展开,而与传统研究不同,本文在此基础上将企业间不合作策略细分为竞争策略和中立策略。以多功能开放型供需网企业为研究对象,运用演化博弈理论分析方法,通过构建供需网企业合作演化博弈模型,进而分析供需网企业合作过程中策略的选择以及博弈演化路径问题。研究结果表明:在长期的演化博弈过程中,企业策略的选择情形出现不稳定现象,即出现完全合作、完全不合作或者一方合作而另一方选择不合作策略的多种状态,其演化路径最终稳定于何种情形与模型的支付矩阵和初始参数设置有关。     

Mean-Variance Hedging Under Multiple Defaults Risk

We solve a mean-variance hedging problem in an incomplete market where multiple defaults can occur. For this purpose, we use a default-density modeling approach. The global market information is formulated as a progressive enlargement of a default-free Brownian filtration, and the dependence of the default times is modelled using a conditional density hypothesis. We prove the quadratic form of each value process between consecutive default times and recursively solve systems of coupled quadratic backward stochastic differential equations (BSDEs). We demonstrate the existence of these solutions using BSDE techniques. Then, using a verification theorem, we prove that the solutions of each subcontrol problem are related to the solution of our global mean-variance hedging problem. As a byproduct, we obtain an explicit formula for the optimal trading strategy. Finally, we illustrate our results for certain specific cases and for a multiple defaults case in particular.     

需求风险下套期保值与市场进入分析

需求风险是企业面临的主要风险之一,对企业的生产经营和管理决策具有重要影响。本文考虑由多个风险厌恶企业构成的产品竞争市场,分析了需求风险下企业参与套期保值和市场进入的决策问题。文章首先通过Cournot博弈分析了套期保值对于规避需求风险的作用和意义;然后,探讨了企业参与套期保值和市场进入的决策过程,并给出了三种情形下的市场均衡结构;最后,通过数值实验对结论进行了验证。研究表明:套期保值提高了企业应对需求风险的能力,使企业获得更高的产量和收益;参与套期保值企业数量随着进入市场企业数量的增加而减少;当市场竞争程度或市场费用增加时,将会有更多的企业选择参与套期保值,而选择进入市场的企业会减少。     

Monte Carlo construction of hedging strategies against multi-asset European claims

For evaluating a hedging strategy we have to know at every moment the solution of the Cauchy problem for a corresponding parabolic equation (the value of the hedging portfolio) and its derivatives (the deltas). We suggest to find these quantities by Monte Carlo simulation of the corresponding system of stochastic differential equations using weak solution schemes. It turns out that with one and the same control function a variance reduction can be achieved simultaneously for the claim value as well as for the deltas. As illustrations we consider a Markovian multi-asset model with an instantaneously riskless saving bond and also some applications to the LIBOR rate model of Brace, Gatarck, Musiela and Jamshidian.     

Cooperative Hedging in the Complete Market under g-expectation Constraint

The paper studies the muiti-agent cooperative hedging problem of contingent claims in the complete market when the g-expected shortfall risks are bounded. We give the optimal cooperative hedging strategy explicitly by the Neyman-Pearson lemma under g-probability.     

On dominance core and stable sets for cooperative ellipsoidal games

Abstract

The allocation problem of rewards or costs is a central question for individuals and organizations contemplating cooperation under uncertainty. The involvement of uncertainty in cooperative games is motivated by the real world where noise in observation and experimental design, incomplete information and further vagueness in preference structures and decision-making play an important role. The theory of cooperative ellipsoidal games provides a new game theoretical angle and suitable tools for answering this question. In this paper, some solution concepts using ellipsoids, namely the ellipsoidal imputation set, the ellipsoidal dominance core and the ellipsoidal stable sets for cooperative ellipsoidal games, are introduced and studied. The main results contained in the paper are the relations between the ellipsoidal core, the ellipsoidal dominance core and the ellipsoidal stable sets of such a game.     

Quadratic Hedging Methods for Defaultable Claims

We apply the local risk-minimization approach to defaultable claims and we compare it with intensity-based evaluation formulas and the mean-variance hedging. We solve analytically the problem of finding respectively the hedging strategy and the associated portfolio for the three methods in the case of a default put option with random recovery at maturity.     

Minimizing coherent risk measures of shortfall in discrete‐time models with cone constraints

The paper studies the problem of minimizing coherent risk measures of shortfall for general discrete‐time financial models with cone‐constrained trading strategies, as developed by Pham and Touzi. It is shown that the optimal strategy is obtained by super‐hedging a contingent claim, which is represented as a Neyman–Pearson‐type random variable.