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Discussiones Mathematicae Probability and Statistics

2005 | 25 | 1 | 51-70
Tytuł artykułu

Optimal trend estimation in geometric asset price models

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the general geometric asset price model, the asset price P(t) at time t satisfies the relation
$P(t) = P₀ · e^{α·f(t) + σ·F(t)}$, t ∈ [0,T],
where f is a deterministic trend function, the stochastic process F describes the random fluctuations of the market, α is the trend coefficient, and σ denotes the volatility.
The paper examines the problem of optimal trend estimation by utilizing the concept of kernel reproducing Hilbert spaces. It characterizes the class of trend functions with the property that the trend coefficient can be estimated consistently. Furthermore, explicit formulae for the best linear unbiased estimator α̂ of α and representations for the variance of α̂ are derived.
The results do not require assumptions on finite-dimensional distributions and allow of jump processes as well as exogeneous shocks. .
Słowa kluczowe
EN
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
51-70
Opis fizyczny
Daty
wydano
2005
otrzymano
2004-01-15
Twórcy
autor
• University of Applied Sciences, Fulda, Marquardstr. 35, D-36039 Fulda, Germany
Bibliografia
• [1] M. Atteia, Hilbertian Kernels and Spline Functions, North-Holland, Amsterdam 1992.
• [2] S. Cambanis, Sampling Designs for Time Series, Time Series in the Time Domain, Handbook of Statistics 5 (1985), (Eds. E.J. Hannan, P.R. Krishnaiah, and M.M. Rao), North-Holland, Amsterdam, 337-362.
• [3] J.Y. Campbell, A.W. Lo and A.C. MacKinlay, The Econometrics of Financial Markets, Princeton University Press, Princeton 1997.
• [4] E. Eberlein and U. Keller, Hyperbolic Distributions in Finance, Bernoulli 1 (1995), 281-299.
• [5] I. Karatzas and S.E. Shreve, Methods of Mathematical Finance, Springer, New York 1998.
• [6] M. Loève, Probability Theory II, (4th Edition), Springer, New York 1978.
• [7] R. Merton, On Estimating the Expected Return on the Market: An Exploratory Investigation, Journal of Financial Economics 8 (1980), 323-361.
• [8] E. Parzen, Regression Analysis of Continuous Parameter Time Series, Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability 1 (1961), (Ed. J. Neyman), University of California Press, 469-489.
• [9] J. Sacks and D. Ylvisaker, Designs for Regression Problems with Correlated Errors, The Annals of Mathematical Statistics 37 (1966), 66-89.
• [10] J. Sacks and D. Ylvisaker, Designs for Regression Problems with Correlated Errors: Many Parameters, The Annals of Mathematical Statistics 39 (1968), 46-69.
• [11] J. Sacks and D. Ylvisaker, Designs for Regression Problems with Correlated Errors III, The Annals of Mathematical Statistics 41 (1970), 2057-2074.
• [12] R.J. Serfling, Approximation Theorems of Mathematical Statistics, Wiley 2002.
• [13] Y. Su and S. Cambanis, Sampling Designs for Estimation of a Random Process, Stochastic Processes and Their Applications 46 (1993), 47-89.
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