Portfolio selection under incomplete information

We study an optimal investment problem under incomplete information and power utility. We analytically solve the Bellman equation, and identify the optimal portfolio policy. Moreover, we compare the solution to the value function in the fully observable case, and quantify the loss of utility due to incomplete information.     

A model of interim information sharing under incomplete information

We propose a two-person game-theoretical model to study information sharing decisions at an interim stage when information is incomplete. The two agents have pieces of private information about the state of nature, and that information is improved by combining the pieces. Agents are both senders and receivers of information. There is an institutional arrangement that fixes a transfer of wealth from an agent who lies about her private information. In our model, we show that (1) there is a positive relation between information revelation and the amount of the transfers, and (2) information revelation has a collective action structure, in particular, the incentives of an agent to reveal decrease with respect to the amount of information disclosed by the other.     

On the stability of evolutionary dynamics in games with incomplete information

In an interaction it is possible that one agent has features it is aware of but the opponent is not. These features (e.g. cost, valuation or fighting ability) are referred to as the agent’s type. The paper compares two models of evolution in symmetric situations of this kind. In one model the type of an agent is fixed and evolution works on strategies of types. In the other model every agent adopts with fixed probabilities both types, and type-contingent strategies are exposed to evolution. It is shown that the dynamic stability properties of equilibria may differ even when there are only two types and two strategies. However, in this case the dynamic stability properties are generically the same when the payoff of a player does not depend directly on the type of the opponent. Examples illustrating these results are provided.     

On the stability of evolutionary dynamics in games with incomplete information

In an interaction it is possible that one agent has features it is aware of but the opponent is not. These features (e.g. cost, valuation or fighting ability) are referred to as the agent’s type. The paper compares two models of evolution in symmetric situations of this kind. In one model the type of an agent is fixed and evolution works on strategies of types. In the other model every agent adopts with fixed probabilities both types, and type-contingent strategies are exposed to evolution. It is shown that the dynamic stability properties of equilibria may differ even when there are only two types and two strategies. However, in this case the dynamic stability properties are generically the same when the payoff of a player does not depend directly on the type of the opponent. Examples illustrating these results are provided.     

Forecasting tender price index under incomplete information

Tender price index (TPI) is essential for estimating the likely tender price of a given project. Due to incomplete information on future market conditions, it is difficult to accurately forecast the TPI. Most traditional statistical forecasting models require a certain number of historical data, which may not be completely available in many practical situations. In order to overcome this problem, the grey model is proposed for forecasting TPIs because it only requires a small number of input data. For this study, the data source was based on the TPIs produced by the Government's Architectural Services Department. On the basis of four input data, the grey model forecasted TPIs from 1981Q1 to 2011Q4. The mean absolute percentage errors of forecast TPIs in one quarter and two quarters ahead were 3.62 and 7.04%, respectively. In order to assess the accuracy and reliability of the grey model further, the same research method was used to forecast other three TPIs in Hong Kong. The forecasting results of all four TPIs were found to be very good. It was thus concluded that the grey model could be able to produce accurate TPI forecasts for a one-quarter to two-quarter forecast horizon.     

Synthesis of discrete stabilization for a nonlinear stationary control system under incomplete information

The paper presents an algorithm for synthesizing discrete control functions in the case of incomplete information and discrete measurer. Under these control functions, solutions of a wide class of nonlinear stationary systems are transferred from the given initial state into an arbitrary neighborhood of the origin with due account taken of the constraints imposed on the control. Constructive criteria for the selection of the initial states and discretization step are derived, which ensure implementation of the suggested algorithm. The efficiency of the method is illustrated with numerical simulation of the problem of interorbital transfer.     

Interest rate options valuation under incomplete information

This paper aims at examining the term structure of interest rates and European-type interest rate option prices in a partially observable economy. It extends the existing literature on incomplete information by developing a one-factor model which is consistent with the initial yield curve and by providing closed-form solutions for discount bonds and different kinds of options. The model of this paper encompasses Hull and White’s (1990). Moreover, through a numerical example, these two models are compared and the impact of incomplete information on option prices is analysed. This article was completed when the author was at the University of Cergy-Pontoise. He is now at the University of Paris 1 Panth éon-Sorbonne, PRISM, 17, rue de la Sorbonne, 75231 Paris Cedex 05. e-mail: constantin.mellios@univ-paris1.fr.     

Families of relations modelling preferences under incomplete information

Let us consider a preferential information of type preference–indifference–incomparability (P, I, J), with additional information about differences in attractiveness between pairs of alternatives. The present paper offers a theoretical framework for the study of the “level of constraint” of this kind of partial preferential information. It suggests a number of structures as potential models being less demanding than the classical one in which differences in utilities can be used to represent the comparison of differences in attractiveness. The models are characterized in the more general context of families of non-complete preference structures, according to two different perspectives (called “semantico-numerical” and “matrix”). Both perspectives open the door to further practical applications connected with elicitation of the preferences of a decision maker.     

Firms' R&D decisions under incomplete information

The paper considers a patent race in which firms do not know their relative positions. In this setting, firms that start in the same position proceed at the highest possible speed; and if one firm has an initial advantage it preempts the rival, but at the cost of dissipating a significant part of its monopoly rent. So the paper shows that incomplete information in a patent race leads to rent dissipation. The latter is higher, the higher the value of the prize and the lower the cost of R&D. Thus, for innovations that provide relatively high profits the time to discovery is shortened, but the social losses are likely to be high, due to duplication of effort.     

On sequential and simultaneous contributions under incomplete information

When contributors to a common cause (or public good) are uncertain about each others’ valuations, early contributors are likely to be cautious in free-riding on future contributors. Contrary to the case of complete information, when contributors have independent private valuations for the public good, the expected total contribution generated in a sequential move game may be higher than in a simultaneous move game. This is established in a conventional framework with quasi-linear utility where agents care only about the total provision of the public good (rather than individual contribution levels) and there is no non-convexity in the provision of the public good. We allow for arbitrary number of agents and fairly general distribution of types.     

On a guaranteed guidance problem under incomplete information

We discuss the problem of guaranteed guidance of a linear control system by a fixed time under the assumption that the system is subject to an unknown disturbance. We consider the case when a part of state coordinates are measured and the set of unknown initial states is finite. We specify a solution algorithm based on the combination of the package approach, the theory of dynamic inversion, and the extremal shift method.     

Sourcing under incomplete information and negative capacity-cost correlation

We study a sourcing problem where a buyer reserves capacity from a set of suppliers. The suppliers have finite capacity and their unit production cost is a decreasing function of their capacity, implying scale economies. The capacity of each supplier and therefore the cost is his private information. The buyer and other suppliers only know the probability distribution of the supplier’s capacity. The buyer’s demand is random and she has to decide how much capacity to reserve in advance from a subset of suppliers and how much to source from marketplace. In this study we determine the buyer’s optimum reservation quantity and the size of the supply base. We find the presence of such capacity cost correlation leads to supply base reduction.     

Dynamic consistency in incomplete information games under ambiguity

We develop a general framework of incomplete information games under ambiguity which extends the traditional framework of Bayesian games to the context of Ellsberg-type ambiguity. We then propose new solution concepts called ex ante and interim Γ-maximin equilibrium for solving such games. We show that, unlike the standard notion of Bayesian Nash equilibrium, these concepts may lead to rather different recommendations for the same game under ambiguity. This phenomenon is often referred to as dynamic inconsistency. Moreover, we characterize the sufficient condition under which dynamic consistency is assured in this generalized framework.     

How to estimate the Value at Risk under incomplete information

A key problem in financial and actuarial research, and particularly in the field of risk management, is the choice of models so as to avoid systematic biases in the measurement of risk. An alternative consists of relaxing the assumption that the probability distribution is completely known, leading to interval estimates instead of point estimates. In the present contribution, we show how this is possible for the Value at Risk, by fixing only a small number of parameters of the underlying probability distribution. We start by deriving bounds on tail probabilities, and we show how a conversion leads to bounds for the Value at Risk. It will turn out that with a maximum of three given parameters, the best estimates are always realized in the case of a unimodal random variable for which two moments and the mode are given. It will also be shown that a lognormal model results in estimates for the Value at Risk that are much closer to the upper bound than to the lower bound.     

How to make sense of the common prior assumption under incomplete information

Recent contributions have questioned the meaningfulness of the Common Prior Assumption (CPA) in situations of incomplete information. We characterize the CPA in terms of the primitives (individuals' belief hierarchies) without reference to an ex ante stage. The key is to rule out “agreeing to disagree” about any aspect of beliefs. Our results also yield a generalization of single-person Bayesian updating to situations without perfect recall. The entire analysis is carried out locally at the “true state”, using beliefs only, rather than beliefs-plus-knowledge. We discuss the role of truth assumptions on beliefs for a satisfactory notion of the CPA, and point out an important conceptual discontinuity between the case of two and many individuals.     

An optimal inspection and replacement policy under incomplete state information

This paper investigates an optimal inspection and replacement problem for a discrete-time Markovian deterioration system. It is assumed that the system is monitored incompletely by a certain mechanism which gives the decision maker some information about the exact state of the system. The problem is to obtain an optimal inspection and replacement policy minimizing the expected total discounted cost over an infinite horizon and formulated as a partially observable Markov decision process. Furthermore, under some reasonable conditions reflecting the practical meaning of the deterioration, it is shown that there exists an optimal inspection and replacement policy in the class of monotonic four-region policies.     

Optimal harvesting policy of an inland fishery resource under incomplete information

A new mathematical model for finding the optimal harvesting policy of an inland fishery resource under incomplete information is proposed in this paper. The model is based on a stochastic control formalism in a regime‐switching environment. The incompleteness of information is due to uncertainties involved in the body growth rate of the fishery resource: a key biological parameter. Finding the most cost‐effective harvesting policy of the fishery resource ultimately reduces to solving a terminal and boundary value problem of a Hamilton‐Jacobi‐Bellman equation: a nonlinear and degenerate parabolic partial differential equation. A simple finite difference scheme for solving the equation is then presented, which turns out to be convergent and generates numerical solutions that comply with certain theoretical upper and lower bounds. The model is finally applied to the management of Plecoglossus altivelis, a major inland fishery resource in Japan. The regime switching in this case is due to the temporal dynamics of benthic algae, the main food of the fish. Model parameter values are identified from field measurement results in 2017. Our computational results clearly show the dependence of the optimal harvesting policy on the river environmental and biological conditions. The proposed model would serve as a mathematical tool for fishery resource management under uncertainties.     

Multi‐period mean variance portfolio selection under incomplete information

This paper solves an optimal portfolio selection problem in the discrete‐time setting where the states of the financial market cannot be completely observed, which breaks the common assumption that the states of the financial market are fully observable. The dynamics of the unobservable market state is formulated by a hidden Markov chain, and the return of the risky asset is modulated by the unobservable market state. Based on the observed information up to the decision moment, an investor wants to find the optimal multi‐period investment strategy to maximize the mean‐variance utility of the terminal wealth. By adopting a sufficient statistic, the portfolio optimization problem with incompletely observable information is converted into the one with completely observable information. The optimal investment strategy is derived by using the dynamic programming approach and the embedding technique, and the efficient frontier is also presented. Compared with the case when the market state can be completely observed, we find that the unobservable market state does decrease the investment value on the risky asset in average. Finally, numerical results illustrate the impact of the unobservable market state on the efficient frontier, the optimal investment strategy and the Sharpe ratio. Copyright © 2016 John Wiley & Sons, Ltd.     

Reconstruction of external actions under incomplete information in a linear stochastic equation

The problem of reconstructing unknown external actions in a linear stochastic differential equation is investigated on the basis of the approach of the theory of dynamic inversion. We consider the statement when the simultaneous reconstruction of disturbances in the deterministic and stochastic terms of the equation is performed with the use of discrete information on a number of realizations of a part of coordinates of the stochastic process. The problem is reduced to an inverse problem for systems of ordinary differential equations describing the mathematical expectation and covariance matrix of the original process. A finite-step software-oriented solution algorithm based on the method of auxiliary controlled models is proposed. We derive an estimate for its convergence rate with respect to the number of measured realizations.