Strong Innovation and its Applications to Information Diffusion Modelling in Finance

2002 ◽  
Vol 9 (2) ◽  
pp. 383-402
Author(s):  
T. Toronjadze
Keyword(s):  
Stock Price ◽  
Information Diffusion ◽  
Utility Maximization ◽  
Partial Information ◽  
Innovation Process ◽  
Full Information ◽  
Diffusion Modelling ◽  
Price Process ◽  
The Mean ◽  
Mean Variance

Abstract We consider the mean-variance hedging and utility maximization problems under partial information for diffusion models of the stock price process. The special feature of this paper is that we construct a strong innovation process for the stock price process which allows us to reduce the partial information case to the full information one.

INCOMPLETE INFORMATION WITH RECURSIVE PREFERENCES

2001 ◽  
Vol 04 (02) ◽  
pp. 245-261 ◽  
Author(s):  
JAKSA CVITANIĆ ◽  
ALI LAZRAK ◽  
MARIE CLAIRE QUENEZ ◽  
FERNANDO ZAPATERO
Keyword(s):  
Stock Price ◽  
Partial Information ◽  
Full Information ◽  
Random Drift ◽  
Recursive Preferences ◽  
Price Process ◽  
Special Cases ◽  
Information Problem ◽  
Price History ◽  
Differential Utility

We consider the case of an agent with recursive preferences (Stochastic Differential Utility or SDU) who cannot observe the random drift of the stock price process. This partial information problem can be transformed into a problem with full information, in which the drift is replaced by its expected value conditional on the information given by the stock price history. We are then in a position to use recent results for maximizing SDUs under full information and their connection to Forward-Backward Stochastic Differential Equations. They enable us to study qualitative differences between the cases with full and partial information. We also analyze some special cases in which we obtain semi-explicit results and compute the SDU numerically.

scholarly journals Continuous-Time Mean-Variance Portfolio Selection under the CEV Process

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Hui-qiang Ma
Keyword(s):  
Portfolio Selection ◽  
Continuous Time ◽  
Stock Price ◽  
Efficient Frontier ◽  
Optimal Portfolio ◽  
Portfolio Strategy ◽  
Cev Process ◽  
The Mean ◽  
Mean Variance Portfolio ◽  
Mean Variance

We consider a continuous-time mean-variance portfolio selection model when stock price follows the constant elasticity of variance (CEV) process. The aim of this paper is to derive an optimal portfolio strategy and the efficient frontier. The mean-variance portfolio selection problem is formulated as a linearly constrained convex program problem. By employing the Lagrange multiplier method and stochastic optimal control theory, we obtain the optimal portfolio strategy and mean-variance efficient frontier analytically. The results show that the mean-variance efficient frontier is still a parabola in the mean-variance plane, and the optimal strategies depend not only on the total wealth but also on the stock price. Moreover, some numerical examples are given to analyze the sensitivity of the efficient frontier with respect to the elasticity parameter and to illustrate the results presented in this paper. The numerical results show that the price of risk decreases as the elasticity coefficient increases.

MEAN VARIANCE HEDGING IN A GENERAL JUMP MARKET

2010 ◽  
Vol 13 (05) ◽  
pp. 789-820
Author(s):  
DEWEN XIONG ◽  
MICHAEL KOHLMANN
Keyword(s):  
Financial Market ◽  
Martingale Measure ◽  
Contingent Claim ◽  
Predictable Process ◽  
Price Process ◽  
The Mean ◽  
Hedging Problem ◽  
Mean Variance ◽  
Intuitive Interpretation ◽  
Density Process

We consider a financial market in which the discounted price process S is an ℝd-valued semimartingale with bounded jumps, and the variance-optimal martingale measure (VOMM) Q opt is only known to be a signed measure. We give a backward semimartingale equation (BSE) and show that the density process Z opt of Q opt with respect to P is a possibly non-positive stochastic exponential if and only if this BSE has a solution. For a general contingent claim H, we consider the following generalized version of the classical mean-variance hedging problem [Formula: see text] where [Formula: see text]. We represent the optimal strategy and the optimal cost of the mean-variance hedging by means of another backward martingale equation (BME) and an appropriate predictable process δ both with a straightforward intuitive interpretation.

scholarly journals MONTE CARLO DERIVATIVE PRICING WITH PARTIAL INFORMATION IN A CLASS OF DOUBLY STOCHASTIC POISSON PROCESSES WITH MARKS

2012 ◽  
Vol 15 (03) ◽  
pp. 1250018
Author(s):  
SILVIA CENTANNI ◽  
MARCO MINOZZO
Keyword(s):  
Monte Carlo ◽  
Stock Price ◽  
Partial Information ◽  
Poisson Processes ◽  
Martingale Measure ◽  
Contingent Claim ◽  
Filtering Algorithm ◽  
Doubly Stochastic ◽  
Price Process ◽  
Monte Carlo Approximation

To model intraday stock price movements we propose a class of marked doubly stochastic Poisson processes, whose intensity process can be interpreted in terms of the effect of information release on market activity. Assuming a partial information setting in which market agents are restricted to observe only the price process, a filtering algorithm is applied to compute, by Monte Carlo approximation, contingent claim prices, when the dynamics of the price process is given under a martingale measure. In particular, conditions for the existence of the minimal martingale measure Q are derived, and properties of the model under Q are studied.

UTILITY MAXIMIZATION WITH INTERMEDIATE CONSUMPTION UNDER RESTRICTED INFORMATION FOR JUMP MARKET MODELS

2012 ◽  
Vol 15 (06) ◽  
pp. 1250040 ◽  
Author(s):  
CLAUDIA CECI
Keyword(s):  
Stock Price ◽  
Utility Maximization ◽  
Backward Stochastic Differential Equation ◽  
Asset Price ◽  
Random Measure ◽  
Innovation Process ◽  
Factor X ◽  
Power Utility ◽  
Intermediate Consumption ◽  
Filtering Problem

The contribution of this paper is twofold: we study power utility maximization problems (with and without intermediate consumption) in a partially observed financial market with jumps and we solve by the innovation method the arising filtering problem. We consider a Markovian model where the risky asset dynamics St follows a pure jump process whose local characteristics are not observable by investors. More precisely, the stock price process dynamics depends on an unobservable stochastic factor Xt described by a jump-diffusion process. We assume that agents' decisions are based on the knowledge of an information flow, [Formula: see text], containing the asset price history, [Formula: see text]. Using projection on the filtration [Formula: see text], the partially observable investment-consumption problem is reduced to a full observable stochastic control problem. The homogeneity of the power utility functions leads to a factorization of the associated value process into a part depending on the current wealth and the so called opportunity process Jt. In the case where [Formula: see text], Jt and the optimal investment-consumption strategy are represented in terms of solutions to a backward stochastic differential equation (BSDE) driven by the [Formula: see text]-compensated martingale random measure associated to St, which can be obtained by filtering techniques (Ceci, 2006; Ceci and Gerardi, 2006). Next, we extend the study to the case [Formula: see text], where ηt gives observations of Xt in additional Gaussian noise. This setup can be viewed as an abstract form of "insider information". The opportunity process Jt is now characterized as a solution to a BSDE driven by the [Formula: see text]-compensated martingale random measure and the so called innovation process. Computation of these quantities leads to a filtering problem with mixed type observation and whose solution is discussed via the innovation approach.

SET-VALUED PERFORMANCE APPROXIMATIONS FOR THE QUEUE GIVEN PARTIAL INFORMATION

2020 ◽  
pp. 1-23
Author(s):  
Yan Chen ◽  
Ward Whitt
Keyword(s):  
Steady State ◽  
Decay Rate ◽  
Waiting Time ◽  
Partial Information ◽  
Upper And Lower Bounds ◽  
Interarrival Time ◽  
Limited Information ◽  
Wide Range ◽  
The Mean ◽  
Third Moment

In order to understand queueing performance given only partial information about the model, we propose determining intervals of likely values of performance measures given that limited information. We illustrate this approach for the mean steady-state waiting time in the $GI/GI/K$ queue. We start by specifying the first two moments of the interarrival-time and service-time distributions, and then consider additional information about these underlying distributions, in particular, a third moment and a Laplace transform value. As a theoretical basis, we apply extremal models yielding tight upper and lower bounds on the asymptotic decay rate of the steady-state waiting-time tail probability. We illustrate by constructing the theoretically justified intervals of values for the decay rate and the associated heuristically determined interval of values for the mean waiting times. Without extra information, the extremal models involve two-point distributions, which yield a wide range for the mean. Adding constraints on the third moment and a transform value produces three-point extremal distributions, which significantly reduce the range, producing practical levels of accuracy.

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