Search results for "Martingale"
showing 10 items of 30 documents
On singular integral and martingale transforms
2007
Linear equivalences of norms of vector-valued singular integral operators and vector-valued martingale transforms are studied. In particular, it is shown that the UMD(p)-constant of a Banach space X equals the norm of the real (or the imaginary) part of the Beurling-Ahlfors singular integral operator, acting on the X-valued L^p-space on the plane. Moreover, replacing equality by a linear equivalence, this is found to be the typical property of even multipliers. A corresponding result for odd multipliers and the Hilbert transform is given.
Value preserving portfolio strategies and the minimal martingale measure
1998
We consider some relations between the minimal martingale measure and the value preserving martingale measure in a continuous-time securities market. Under the assumption of continuous share prices we show that under a structure condition both these martingale measures exist and indeed coincide. This however does not mean that the corresponding concepts of value preserving portfolio strategies and (local) risk minimisation in the area of option hedging in incomplete markets are identical.
Ambit processes and stochastic partial differential equations
2011
Ambit processes are general stochastic processes based on stochastic integrals with respect to Levy bases. Due to their flexible structure, they have great potential for providing realistic models for various applications such as in turbulence and finance. This papers studies the connection between ambit processes and solutions to stochastic partial differential equations. We investigate this relationship from two angles: from the Walsh theory of martingale measures and from the viewpoint of the Levy noise analysis.
A formal proof of the ε-optimality of absorbing continuous pursuit algorithms using the theory of regular functions
2014
Published version of an article from the journal: Applied Intelligence. Also available on Springerlink: http://dx.doi.org/10.1007/s10489-014-0541-1 The most difficult part in the design and analysis of Learning Automata (LA) consists of the formal proofs of their convergence accuracies. The mathematical techniques used for the different families (Fixed Structure, Variable Structure, Discretized etc.) are quite distinct. Among the families of LA, Estimator Algorithms (EAs) are certainly the fastest, and within this family, the set of Pursuit algorithms have been considered to be the pioneering schemes. Informally, if the environment is stationary, their ε-optimality is defined as their abili…
Interpolation and approximation in L2(γ)
2007
Assume a standard Brownian motion W=(W"t)"t"@?"["0","1"], a Borel function f:R->R such that f(W"1)@?L"2, and the standard Gaussian measure @c on the real line. We characterize that f belongs to the Besov space B"2","q^@q(@c)@?(L"2(@c),D"1","2(@c))"@q","q, obtained via the real interpolation method, by the behavior of a"X(f(X"1);@t)@[email protected]?f(W"1)-P"X^@tf(W"1)@?"L"""2, where @t=(t"i)"i"="0^n is a deterministic time net and P"X^@t:L"2->L"2 the orthogonal projection onto a subspace of 'discrete' stochastic integrals x"[email protected]?"i"="1^nv"i"-"1(X"t"""i-X"t"""i"""-"""1) with X being the Brownian motion or the geometric Brownian motion. By using Hermite polynomial expansions the…
Quadratic variation of martingales in Riesz spaces
2014
We derive quadratic variation inequalities for discrete-time martingales, sub- and supermartingales in the measure-free setting of Riesz spaces. Our main result is a Riesz space analogue of Austinʼs sample function theorem, on convergence of the quadratic variation processes of martingales http://www.journals.elsevier.com/journal-of-mathematical-analysis-and-applications/ http://dx.doi.org/10.1016/j.jmaa.2013.08.037 National Research Foundation of South Africa (Grant specific unique reference number (UID) 85672) and by GNAMPA of Italy (U 2012/000574 20/07/2012 and U 2012/000388 09/05/2012)
Testing the Martingale Property of Exchange Rates: A Replication
2010
In this paper, we test the martingale property of a set of U.S. exchange rates already analyzed in a recent paper by Yilmaz [J. of Buss. and Ec. Stat., 2003]. We claim that the tests used by Yilmaz are not the most convenient to test the martingale hypothesis (or the equivalent martingale difference of the returns); hence, we compute a recently proposed test by Kuan and Lee [Stud. in Nonlin. Dyn. and Econ., 2004] and compare our results to Yilmaz's. Striking differences arise, which can give a clue about the type of data generating process governing the evolution of exchange rates in each sub-period.
On Fuzzy Stochastic Integral Equations—A Martingale Problem Approach
2011
In the paper we consider fuzzy stochastic integral equations using the methods of stochastic inclusions. The idea is to consider an associated martingale problem and its solutions in order to obtain a solution to the fuzzy stochastic equation.
Martingale Convergence Theorems and Their Applications
2020
We became familiar with martingales X=(X n ) n∈N0 as fair games and found that under certain transformations (optional stopping, discrete stochastic integral) martingales turn into martingales. In this chapter, we will see that under weak conditions (non-negativity or uniform integrability) martingales converge almost surely. Furthermore, the martingale structure implies L p -convergence under assumptions that are (formally) weaker than those of Chapter 7. The basic ideas of this chapter are Doob’s inequality (Theorem 11.4) and the upcrossing inequality (Lemma 11.3).
Solving stochastic differential equations on Homeo(S1)
2004
Abstract The Brownian motion with respect to the metric H 3/2 on Diff( S 1 ) has been constructed. It is realized on the group of homeomorphisms Homeo( S 1 ). In this work, we shall resolve the stochastic differential equations on Homeo( S 1 ) for a given drift Z .