This paper is concerned with the optimal control problem,where the recursive cost functional is defined as one of the solution to a controlled fully coupled forward-backward stochastic differential equation（FBSDE）,a...
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This paper is concerned with the optimal control problem,where the recursive cost functional is defined as one of the solution to a controlled fully coupled forward-backward stochastic differential equation（FBSDE）,and the control domain is *** different approaches–dynamic programming principle（DPP） and maximum principle（MP）–are applied to solve the problem and the relationship between them are *** some differentiable assumptions,relations among the adjoint processes,the value function and the generalized Hamiltonian function are proved,whereas the diffusion term of the forward equation is independent of the state variable *** general case for the problem is open.A linear example is discussed as the illustration of our main result.
＜正＞One kind of corporate optimal portfolio and consumption choice problem is studied for a investor who can invest his wealth in the bond （bank account） and in a real project which has the production. The bank pa...
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＜正＞One kind of corporate optimal portfolio and consumption choice problem is studied for a investor who can invest his wealth in the bond （bank account） and in a real project which has the production. The bank pays at an interest rate for any deposit and takes at a large rate for any loan. The optimal strategies are obtained by Hamilton-Jacobi-Bell-man equation which is derived from dynamic programming principle. We also give the economic analysis to the optimal choice using the investment theory. For the specific Hyperbolic Absolute Risk Aversion case, we get the explicit optimal investment and consumption solution. At last, we give some simulation results to illustrate the optimal result and the influence of the volatility parameter on the optimal choice.
This paper develops a model for the bid and ask prices of a European-type asset by formulating a stochastic control problem. The state process is governed by a modified geometric Brownian motion whose drift and diffus...
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This paper develops a model for the bid and ask prices of a European-type asset by formulating a stochastic control problem. The state process is governed by a modified geometric Brownian motion whose drift and diffusion coefficients depend on a Markov chain. A Girsanov theorem for Markov chains is implemented for the change of coefficients, including the diffusion coefficient which cannot be changed by the usual Girsanov theorem for Brownian motion. The price of a European-type asset is then determined using an Esscher transform and a system of partial differential equations. A dynamic programming principle and a maximum/minimum principle associated with the stochastic control problem are then derived to model bid and ask prices. These prices are not quotes of traders or market makers but represent estimates in our model on which reasonable quantities could be traded.
This paper analyzes zero sum game involving hybrid controls using viscosity solution theory where both players use discrete as well as continuous controls. We study two problems, one in finite horizon and other in inf...
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This paper analyzes zero sum game involving hybrid controls using viscosity solution theory where both players use discrete as well as continuous controls. We study two problems, one in finite horizon and other in infinite horizon. In both cases, we allow the cost functionals to be unbounded with certain growth, hence the corresponding lower and upper value functions defined in Elliot-Kalton sense can be unbounded. We characterize the value functions as the unique viscosity solution of the associated lower and upper quasi variational inequalities in a suitable function class. Further we find a condition under which the game has a value for both games. The major difficulties arise due to unboundedness of value function. In infinite horizon case we prove uniqueness of viscosity solution by converting the unbounded value function into bounded ones by suitable transformation. In finite horizon case an argument is based on comparison with a supersolution.
Pension schemes all over the world are under increasing pressure to efficiently hedge longevity risk imposed by ageing populations. In this work, we study an optimal investment problem for a defined contribution pensi...
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Pension schemes all over the world are under increasing pressure to efficiently hedge longevity risk imposed by ageing populations. In this work, we study an optimal investment problem for a defined contribution pension scheme that decides to hedge longevity risk using a mortality-linked security, typically a longevity bond. The pension scheme promises a minimum guarantee which allows the members to purchase lifetime annuities upon retirement. The scheme manager invests in the risky and riskless assets available on the market, including the longevity bond. We transform the corresponding constrained optimal investment problem into a single investment portfolio optimization problem by replicating future contributions from members and the minimum guarantee provided by the scheme. We solve the resulting optimization problem using the dynamic programming principle. Through a series of numerical studies, we show that the longevity risk has an important impact on the investment strategy performance. Our results add to the growing evidence supporting the use of mortality-linked securities for efficient hedging of longevity risk.
This paper is split in three parts: first, we use labeled trade data to exhibit how market participants' decisions depend on liquidity imbalance;then, we develop a stochastic control framework where agents monitor...
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This paper is split in three parts: first, we use labeled trade data to exhibit how market participants' decisions depend on liquidity imbalance;then, we develop a stochastic control framework where agents monitor limit orders, by exploiting liquidity imbalance, to reduce adverse selection. For limit orders, we need optimal strategies essentially to find a balance between fast execution and avoiding adverse selection: if the price has chances to go down, the probability to be filled is high, but it is better to wait a little more to get a better price. In a third part, we show how the added value of exploiting liquidity imbalance is eroded by latency: being able to predict future liquidity consuming owsis of less use if you do not have enough time to cancel and reinsert your limit orders. There is thus a rationale for market makers to be as fast as possible to reduce adverse selection. Latency costs of our limit order driven strategy can be measured numerically. To authors' knowledge, this paper is the first to make the connection between empirical evidences, a stochastic framework for limit orders including adverse selection, and the cost of latency. Our work is a first step to shed light on the role played by latency and adverse selection in optimal limit order placement.
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