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

Anh, Vo; Inoue, Akihiko; Kasahara, Yukio

doi:10.1081/sap-200050099

Cited by 23 publications

(28 citation statements)

References 15 publications

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“…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.…”

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confidence: 99%

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Financial Markets with Memory I: Dynamic Models

Anh

Inoue

2005

Stochastic Analysis and Applications

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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.

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Section: Proposition 32 Suppose That There Exists a Positive Constamentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Financial Markets with Memory I: Dynamic Models

Anh

Inoue

2005

Stochastic Analysis and Applications

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“…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

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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.

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A Learning Model with Memory in the Financial Markets

Singh,

Chandrasena,

Shi

et al. 2024

Int. J Fin Econ

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Learning is central to a financial agent's aspiration to gain persistent strategic advantage in asset value maximisation. The implicit mechanism that transforms this aspiration into an observed value gain is the speed of error corrections (demonstrating, an agent's speed of learning) whilst facing increased uncertainty. In such a setting, perpetual learning can lead to a type of memory that financial agents can exploit as an information set to plan for their next strategic decisions. The existing literature focuses predominantly on a learning model with a long‐lag characterisation of asset values. However, recent methodological advances show that long memory can be generated from a learning model with just one lag. In this paper, we exploit this strand of literature and integrate the new construct into our proposed duration‐compliant ‘social distance’ mechanic as an alternative robust model of learning in a financial market. We assess the efficacy of our approach with a numerical example and a calibration exercise.

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

Cited by 23 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

A Learning Model with Memory in the Financial Markets

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