Financial Markets with Memory II: Innovation Processes and Expected Utility Maximization

Anh, Vo; Inoue, Akihiko; Kasahara, Yukio

doi:10.1081/sap-200050099

Cited by 22 publications

(28 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To explicitly solve the same problem for the financial market M above, we need to calculate the conditional expectation α(t) = E[U (t)|F(t)] in (3.4) explicitly. This will be done in [3].…”

Section: Proposition 32 Suppose That There Exists a Positive Constamentioning

confidence: 99%

“…This fact turns out to be a great advantage of the model, as will be illustrated in our second paper [3] in which methods of calculating conditional expectations relevant to Y (·) are developed. This is done by applying a new method for prediction, in which both AR(∞)-and MA(∞)-type representations play an important role.…”

mentioning

confidence: 99%

“…In particular, we can define the SDE (1.1). The explicit form of the semimartingale representation will be derived in [3]. It should be noticed that (1.4) or (1.5) is not a semimartingale representation of Y (·) since the Brownian motion W (·) is not {F (t)}-adapted.…”

mentioning

confidence: 99%

“…This is done by applying a new method for prediction, in which both AR(∞)-and MA(∞)-type representations play an important role. In [3], the semimartingale representation of Y (·) is derived in explicit form by the method, and, by applying the representation, the expected log-utility maximization problem for the financial market model is solved completely.…”

mentioning

confidence: 99%

See 3 more Smart Citations

Financial Markets with Memory I: Dynamic Models

Anh

Inoue

2005

Stochastic Analysis and Applications

Self Cite

View full text Add to dashboard Cite

Abstract. This is the first of two papers in which we consider a stock with price process defined by a stochastic differential equation driven by a process Y (·) different from Brownian motion. The adoption of such a colored noise input is motivated by an analysis of real market data. The process Y (·) is defined by a continuous-time AR(∞)-type equation and may have either short or long memory. We show that the process Y (·) has a good MA(∞)-type representation. The existence of such simultaneous good AR(∞) and MA(∞) representations enables us to apply a new method for the calculation of relevant conditional expectations, whence to obtain various explicit results for problems such as portfolio optimization. The financial market defined by the above stock price process is complete, and if the coefficients are constant, then the prices of European calls and puts are given by the Black-Scholes formulas as in the Black-Scholes model. Unlike the latter, however, the model allows for differences between the historical and implied volatilities. The model includes a special case in which only two additional parameters are introduced to describe the memory of the market, compared with the Black-Scholes model. Analysis based on real market data shows that this simple model with two additional parameters is more realistic in capturing the memory effect of the market, while retaining the simplicity and usefulness of the Black-Scholes model.

show abstract

Section: Proposition 32 Suppose That There Exists a Positive Constamentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Financial Markets with Memory I: Dynamic Models

Anh

Inoue

2005

Stochastic Analysis and Applications

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the special case p j = 0, Y j (t) reduces to the Brownian motion W j (t). Driving noise processes with short or long memory of this kind are considered in [1], Anh et al [2] and Inoue et al [20], for the case n = 1. We define…”

Section: Introductionmentioning

confidence: 99%

Optimal Long-Term Investment Model with Memory

Inoue

Nakano

2006

Appl Math Optim

View full text Add to dashboard Cite

Abstract. We consider a financial market model driven by an R n -valued Gaussian process with stationary increments which is different from Brownian motion. This driving noise process consists of n independent components, and each component has memory described by two parameters. For this market model, we explicitly solve optimal investment problems. These include (i) Merton's portfolio optimization problem; (ii) the maximization of growth rate of expected utility of wealth over the infinite horizon; (iii) the maximization of the large deviation probability that the wealth grows at a higher rate than a given benchmark. The estimation of paremeters is also considered.

show abstract

Stochastic Functional Differential Equations and Sensitivity to Their Initial Path

Baños

Nunno

Haferkorn

et al. 2018

Computation and Combinatorics in Dynamics, Stochastics and Control

View full text Add to dashboard Cite

We consider systems with memory represented by stochastic functional differential equations. Substantially, these are stochastic differential equations with coefficients depending on the past history of the process itself. Such coefficients are hence defined on a functional space. Models with memory appear in many applications ranging from biology to finance. Here we consider the results of some evaluations based on these models (e.g. the prices of some financial products) and the risks connected to the choice of these models. In particular we focus on the impact of the initial condition on the evaluations. This problem is known as the analysis of sensitivity to the initial condition and, in the terminology of finance, it is referred to as the Delta. In this work the initial condition is represented by the relevant past history of the stochastic functional differential equation. This naturally leads to the redesign of the definition of Delta. We suggest to define it as a functional directional derivative, this is a natural choice. For this we study a representation formula which allows for its computation without requiring that the evaluation functional is differentiable. This feature is particularly relevant for applications. Our formula is achieved by studying an appropriate relationship between Malliavin derivative and functional directional derivative. For this we introduce the technique of randomisation of the initial condition.

show abstract

Financial Markets with Memory II: Innovation Processes and Expected Utility Maximization

Cited by 22 publications

References 15 publications

Financial Markets with Memory I: Dynamic Models

Financial Markets with Memory I: Dynamic Models

Optimal Long-Term Investment Model with Memory

Stochastic Functional Differential Equations and Sensitivity to Their Initial Path

Contact Info

Product

Resources

About