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1.
Email: nikolaidokuchaev{at}trentu.ca
Received on 27 March 2006. Accepted on 14 September 2007. We study an optimal investment problem for a continuous-timeincomplete market model such that the risk-free rate, the appreciationrates and the volatility of the stocks are all random; theyare not necessarily adapted to the driving Brownian motion,and their distributions are unknown, but they are supposed tobe currently observable. The optimal investment problem is statedin maximin setting which leads to maximizationof the minimum of expected utility over all distributions ofparameters. We found that the presence of the non-discountedwealth in the performance criterion (in addition to the discountedwealth) implies an additional condition for the saddle pointof the maximin problem: the saddle point must include the minimumof the possible risk-free return. This is different from thecase when the utility depends on the discounted wealth only.Using this result, the maximin problem is reduced to a linearparabolic equation and minimization over two scalar parameters.It is an important development of the results obtained in Dokuchaev(2002, Dynamic Portfolio Strategies: Quantitative Methods andEmpirical Rules for Incomplete Information. Boston: Kluwer;2006, IMA J. Manage. Math., 17, 257–276). 相似文献
2.
TRIANTAFILLIDIS S.; LEACH J. A.; OWENS D. H.; TOWNLEY S. 《IMA Journal of Mathematical Control and Information》1996,13(3):251-277
A problem of universal adaptive stabilization in Rn is approachedin a qualitative manner to relate the form of the trajectoriesin the extended state space Rn+1 to the root locus of the associatedfixed-parameter linear system. Relationships are derived betweenthe values of the limit gain and the initial conditions. Numericalstudies are used to illustrate and support these ideas by computationof generic trajectories and attempted computation of certainnon-generic possibilities. The implications of the study formore general dynamic situations are outlined.
These authors are also with the Department of Mathematics,University of Exeter, EX4 4QE. 相似文献
3.
Email: skrakowi{at}usk.pk.edu.pl
Received on June 15, 2005; Accepted on July 12, 2006 In this paper, the time-optimal control problem for parabolicsystems in which time lags appear in the integral form bothin the state equation and in the Neumann boundary conditionis presented. The particular properties of the optimal controlare discussed. 相似文献
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Present address: Department of Mathematics, University of Reading, Reading RG6 2AX. We consider the convergence of solution curves of approximationsto parameter-dependent operator equations of the form G(, x)= 0. Provided Gx(, x) remains non-singular this problem is cateredfor by a simple extension to standard theory. In this paper,however, attention is concentrated on solution curves throughcertain singular points (0, x0), and the main result is thatconvergence depends on consistency and stability results forthe linear eigenvalue problem Gx(0, x0)0 = 0. 相似文献
7.
Let us consider the boundary value problem
where RN is a bounded domain with smooth boundary (for example,such that certain Sobolev imbedding theorems hold). Let :RR, (s)=A(s2)s Then, if (s) = |s|p1s, p > 1, problem (1) is fairlywell understood and a great variety of existence results areavailable. These results are usually obtained using variationalmethods, monotone operator methods or fixed point and degreetheory arguments in the Sobolev space . If, on the other hand, we assume that is an oddnondecreasing function such that (0)=0, (t)>0, t>0,
and is right continuous, then a Sobolev space setting for the problem is not appropriateand very general results are rather sparse. The first generalexistence results using the theory of monotone operators inOrliczSobolev spaces were obtained in [5] and in [9,10]. Other recent work that puts the problem into this frameworkis contained in [2] and [8]. It is in the spirit of these latter papers that we pursue thestudy of problem (1) and we assume that F:xRR is a Carathéodoryfunction that satisfies certain growth conditions to be specifiedlater. We note here that the problems to be studied, when formulatedas operator equations, lead to the use of the topological degreefor multivalued maps (cf. [4, 16]). We shall see that a natural way of formulating the boundaryvalue problem will be a variational inequality formulation ofthe problem in a suitable OrliczSobolev space. In orderto do this we shall have need of some facts about OrliczSobolevspaces which we shall give now. 相似文献
8.
An LMI-based approach for robust stabilization of time delay systems containing saturating actuators
El Haoussi Fatima; Tissir El Houssaine 《IMA Journal of Mathematical Control and Information》2007,24(3):347-356
Email: elhaous_fati{at}yahoo.fr Corresponding author. Email: elh_tissir{at}yahoo.fr
Received on September 8, 2005; Accepted on July 24, 2006 This paper deals with the problem of robust stabilization foruncertain systems with input saturation and time delay in thestate. The parameter uncertainties are time-varying and unknownbut are norm bounded. Sufficient conditions obtained via a linearmatrix inequality formulation are stated to guarantee the localstabilization. The method of synthesis consists in determiningsimultaneously a state feedback control law and an associateddomain of safe admissible states for which the stability ofthe closed-loop system is guaranteed when control saturationseffectively occur. Numerical examples are used to demonstratethe effectiveness of the proposed design technique. 相似文献
9.
Gaussian factor models futures and forward prices 总被引:1,自引:0,他引:1
Email: hyndman{at}mathstat.concordia.ca
Received on 31 July 2006. Accepted on 19 March 2007. We completely characterize the futures price and forward priceof a risky asset (commodity) paying a stochastic dividend yield(convenience yield). The asset (commodity) price is modelledas an exponential affine function of a Gaussian factors process,while the interest rate and dividend yield are affine functionsof the factors process. The characterization we provide is basedon the method of stochastic flows. We believe this method leadsto simpler and more clear-cut derivations of the futures priceand forward price formulae than alternative methods. Hedginga long-term forward contract with shorter term futures contractsand bonds is also examined. 相似文献
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In [17, 18, 19], we began to investigate the continuity propertiesof homomorphisms from (non-abelian) group algebras. Alreadyin [19], we worked with general intertwining maps [3, 12]. Thesemaps not only provide a unified approach to both homomorphismsand derivations, but also have some significance in their ownright in connection with the cohomology comparison problem [4]. The present paper is a continuation of [17, 18, 19]; this timewe focus on groups which are connected or factorizable in thesense of [26]. In [26], G. A. Willis showed that if G is a connectedor factorizable, locally compact group, then every derivationfrom L1(G) into a Banach L1(G)-module is automatically continuous.For general intertwining maps from L1(G), this conclusion isfalse: if G is connected and, for some nN, has an infinite numberof inequivalent, n-dimensional, irreducible unitary representations,then there is a discontinuous homomorphism from L1(G into aBanach algebra by [18, Theorem 2.2] (provided that the continuumhypothesis is assumed). Hence, for an arbitrary intertwiningmap from L1(G), the best we can reasonably hope for is a resultasserting the continuity of on a large, preferablydense subspace of L1(G). Even if the target space of is a Banachmodule (which implies that the continuity ideal I() of is closed),it is not a priori evident that is automatically continuous:the proofs of the automatic continuity theorems in [26] relyon the fact that we can always confine ourselves to restrictionsto L1(G) of derivations from M(G) [25, Lemmas 3.1 and 3.4].It is not clear if this strategy still works for an arbitraryintertwining map from L1(G) into a Banach L1(G)-module. 相似文献
11.
Email: valery{at}techunix.technion.ac.il
Received on January 31, 2006; Accepted on October 5, 2006 An infinite horizon linear-quadratic optimal control problemfor a singularly perturbed system with multiple point-wise anddistributed small delays in the state variable is considered.The set of Riccati-type equations, associated with this problemby the control optimality conditions, is studied. Since thesystem in the control problem is singularly perturbed, the equationsof this set are also perturbed by a small parameter of the singularperturbations. The zero-order asymptotic solution to this setof equations is constructed and justified. Based on this asymptoticsolution, parameter-free sufficient conditions for the existenceand uniqueness of solution to the original optimal control problemare established. 相似文献
12.
Email: bahaa_gm{at}hotmail.com
Received on December 6, 2005; Accepted on December 7, 2006 Optimal control problems of systems governed by parabolic equationswith an infinite number of variables and with additional equalityconstraints are considered. The extremum principle, as wellas sufficient condition of optimality, is formulated for theNeumann problem by using certain extensions of Dubovitskii–Milyutinmethod. 相似文献
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Bai Xiaoming; Yang Xiao-Song; Li Huimin 《IMA Journal of Mathematical Control and Information》2007,24(4):483-491
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Wu Ligang; Lam James; Wang Changhong 《IMA Journal of Mathematical Control and Information》2009,26(1):23-44
15.
Let µ be a real number. The Möbius group Gµis the matrix group generated by
It is known that Gµ is free if |µ| 2 (see [1])or if µ is transcendental (see [3, 8]). Moreover, thereis a set of irrational algebraic numbers µ which is densein (2, 2) and for which Gµ is non-free [2, p. 528].We may assume that µ > 0, and in this paper we considerrational µ in (0, 2). The following problem is difficult.
Let Gnf denote the set of all rational numbers µ in (0,2) for which Gµ is non-free. In 1969 Lyndon and Ullman[8] proved that Gnf contains the elements of the forms p/(p2+ 1) and 1/(p + 1), where p = 1, 2, ..., and that if µ0 Gnf, then µ0/p Gnf for p = 1, 2, .... In 1993 Beardon[2] studied problem (P) by means of the words of the form ArBs At and Ar Bs At Bu Av, and he obtained a sufficient conditionfor solvability of (P), included implicitly in [2, pp. 530531],by means of the following Diophantine equations:
1991 Mathematics SubjectClassification 20E05, 20H20, 11D09. 相似文献
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Kuera's completely algebraic method is used to derive a polynomialsolution with only one Diophantine equation for least-squaresdeterministic control in discrete-time. The same method is used,again involving only one Diophantine equation, to derive themultivariable discrete-time Wiener filter.
This paper was presented at the IMA Symposium on Control Theory,Somerville College,Oxford, September 1986. 相似文献
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Let Ratk(CPn) denote the space of based holomorphic maps ofdegree k from the Riemannian sphere S2 to the complex projectivespace CPn. The basepoint condition we assume is that f()=[1,..., 1]. Such holomorphic maps are given by rational functions: Ratk(CPn) ={(p0(z), ..., pn(z)):each pi(z) is a monic, degree-kpolynomial and such that there are no roots common to all pi(z)}.(1.1) The study of the topology of Ratk(CPn) originated in [10]. Later,the stable homotopy type of Ratk(CPn) was described in [3] interms of configuration spaces and Artin's braid groups. LetW(S2n) denote the homotopy theoretic fibre of the Freudenthalsuspension E:S2n S2n+1. Then we have the following sequenceof fibrations: 2S2n+1 W(S2n)S2n S2n+1. A theorem in [10] tellsus that the inclusion Ratk(CPn) 2kCPn 2S2n+1 is a homotopy equivalenceup to dimension k(2n1). Thus if we form the direct limitRat(CPn)= limk Ratk(CPn), we have, in particular, that Rat(CPn)is homotopy equivalent to 2S2n+1. If we take the results of [3] and [10] into account, we naturallyencounter the following problem: how to construct spaces Xk(CPn),which are natural generalizations of Ratk(CPn), so that X(CPn)approximates W(S2n). Moreover, we study the stable homotopytype of Xk(CPn). The purpose of this paper is to give an answer to this problem.The results are stated after the following definition. 1991Mathematics Subject Classification 55P35. 相似文献
19.
Email: csfvega{at}dm.uba.ar
Received on August 17, 2006; Accepted on September 8, 2007 Necessary conditions are proved for optimal control problemsinvolving an infinite horizon and terminal conditions at infinitywhose states are governed by Volterra integral equations withnon-linear time delay. 相似文献
20.
Email: cimatti{at}dm.unipi.it
Received on September 26, 2005; Accepted on August 2, 2006 The problem of finding in the thermistor problem the optimaldifference of applied potential in order to minimize a suitablecost functional involving the temperature is studied. We findthe optimal system in the elementary case of constant electricconductivity. In addition, a theorem of existence of the optimalsolution is given in the general case of conductivities dependingon the temperature. 相似文献