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Random Times (random + time)

Distribution by Scientific Domains

Mathematics and Statistics	33%
Business, Economics, Finance and Accounting	33%

Selected Abstracts

PRICING IN AN INCOMPLETE MARKET WITH AN AFFINE TERM STRUCTURE

MATHEMATICAL FINANCE, Issue 3 2004
Virginia R. Young
We apply the principle of equivalent utility to calculate the indifference price of the writer of a contingent claim in an incomplete market. To recognize the long-term nature of many such claims, we allow the short rate to be random in such a way that the term structure is affine. We also consider a general diffusion process for the risky stock (index) in our market. In a complete market setting, the resulting indifference price is the same as the one obtained by no-arbitrage arguments. We also show how to compute indifference prices for two types of contingent claims in an incomplete market, in the case for which the utility function is exponential. The first is a catastrophe risk bond that pays a fixed amount at a given time if a catastrophe does not occur before that time. The second is equity-indexed term life insurance which pays a death benefit that is a function of the short rate and stock price at the random time of the death of the insured. Because we assume that the occurrence of the catastrophe or the death of the insured is independent of the financial market, the markets for the catastrophe risk bond and the equity-indexed life insurance are incomplete. [source]

Some bounds on the coupon collector problem

RANDOM STRUCTURES AND ALGORITHMS, Issue 2 2004
Servet Martinez
Abstract This work addresses on the coupon collector problem and its generalization introduced by Flajolet, Gardy, and Thimonier. In our main results, we show a ratio limit theorem for the random time of the generalized coupon collector problem, and, further, we give the leading term and the geometric rate for the distribution of this random time, when the number of throws is large. For the classical coupon collector problem, we give a bound on the conditional second moment for the number of visits to the coupons, relying strongly on a result of Holst on extremal distributions. © 2004 Wiley Periodicals, Inc. Random Struct. Alg. 2004 [source]

Financial Innovation and the Transactions Demand for Cash

ECONOMETRICA, Issue 2 2009
Fernando Alvarez
We document cash management patterns for households that are at odds with the predictions of deterministic inventory models that abstract from precautionary motives. We extend the Baumol,Tobin cash inventory model to a dynamic environment that allows for the possibility of withdrawing cash at random times at a low cost. This modification introduces a precautionary motive for holding cash and naturally captures developments in withdrawal technology, such as the increasing diffusion of bank branches and ATM terminals. We characterize the solution of the model, which qualitatively reproduces several empirical patterns. We estimate the structural parameters using micro data and show that quantitatively the model captures important economic patterns. The estimates are used to quantify the expenditure and interest rate elasticity of money demand, the impact of financial innovation on money demand, the welfare cost of inflation, and the benefit of ATM ownership. [source]

Strategic Experimentation with Exponential Bandits

ECONOMETRICA, Issue 1 2005
Godfrey Keller
We analyze a game of strategic experimentation with two-armed bandits whose risky arm might yield payoffs after exponentially distributed random times. Free-riding causes an inefficiently low level of experimentation in any equilibrium where the players use stationary Markovian strategies with beliefs as the state variable. We construct the unique symmetric Markovian equilibrium of the game, followed by various asymmetric ones. There is no equilibrium where all players use simple cut-off strategies. Equilibria where players switch finitely often between experimenting and free-riding all yield a similar pattern of information acquisition, greater efficiency being achieved when the players share the burden of experimentation more equitably. When players switch roles infinitely often, they can acquire an approximately efficient amount of information, but still at an inefficient rate. In terms of aggregate payoffs, all these asymmetric equilibria dominate the symmetric one wherever the latter prescribes simultaneous use of both arms. [source]

Structural learning with time-varying components: tracking the cross-section of financial time series

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 3 2005
Makram Talih
Summary., When modelling multivariate financial data, the problem of structural learning is compounded by the fact that the covariance structure changes with time. Previous work has focused on modelling those changes by using multivariate stochastic volatility models. We present an alternative to these models that focuses instead on the latent graphical structure that is related to the precision matrix. We develop a graphical model for sequences of Gaussian random vectors when changes in the underlying graph occur at random times, and a new block of data is created with the addition or deletion of an edge. We show how a Bayesian hierarchical model incorporates both the uncertainty about that graph and the time variation thereof. [source]

The effect of annealing on the nonlinear viscoelastic response of isotactic polypropylene

POLYMER ENGINEERING & SCIENCE, Issue 4 2003
Aleksey D. Drozdov
Three series of tensile relaxation tests are performed on isotactic polypropylene at room temperature in the vicinity of the yield point. In the first series of experiments, injection-molded samples are used without thermal pre-treatment. In the second and third series, the specimens are annealed at 130°C for 4 and 24 hours, respectively. Constitutive equations are derived for the time-dependent response of semicrystalline polymers at isothermal loading with small strains. A polymer is treated as an equivalent temporary network of macromolecules bridged by junctions (physical cross-links, entanglements and crystalline lamellae). Under loading, junctions slide with respect to their positions in the bulk material (which reflects the viscoplastic behavior), whereas active strands separate from their junctions and dangling strands merge with the network at random times (which reflects the viscoelastic response). The network is thought of as an ensemble of meso-regions (MRs) with various activation energies for detachment of chains from temporary nodes. Adjustable parameters in the stress-strain relations are found by fitting the observations. The experimental data demonstrate that the relaxation spectrum (characterized by the distribution of MRs with various potential energies) is independent of mechanical factors, but is altered at annealing. For specimens not subjected to thermal treatment, the growth of longitudinal strain does not affect the volume fraction of active MRs and the attempt rate for detachment of chains from their junctions. For annealed samples, the concentration of active MRs increases and the attempt rate decreases with strain. These changes in the time-dependent response are attributed to broadening of the distribution of strengths of lamellae at annealing. [source]

Time-varying changes in corticospinal excitability accompanying the triphasic EMG pattern in humans

THE JOURNAL OF PHYSIOLOGY, Issue 3 2000
Colum D. MacKinnon
1Nine healthy subjects performed single rapid wrist movements from neutral to targets at 20 deg of flexion or extension in response to an auditory cue. Surface EMG was recorded from the wrist flexors and extensors together with wrist position. Movements in both directions were characterised by the usual triphasic pattern of EMG activity in agonist (AG1), antagonist (ANTAG) and again in agonist (AG2) muscles. 2Single pulses of transcranial magnetic stimulation (TMS) were applied over the motor cortex at an intensity of 80 % of resting threshold at random times between 80 and 380 ms after the cue. We measured the peak-to-peak amplitude of the evoked motor potential (MEP) and the integrated EMG (IEMG) activity that preceded the MEP. In a separate set of experiments H reflexes were elicited in the wrist flexors instead of MEPs. 3MEP amplitudes in the agonist muscle increased by an average of 10 ± 8 ms (range ,1 to 23 ms) prior to the onset of the AG1 burst and were associated with an increase of over sevenfold in the MEP:IEMG ratio, irrespective of movement direction. Agonist H reflex amplitudes were linearly related to, and increased at the same time as, changes in agonist IEMG. 4The principal ANTAG burst was not preceded by an increase in the antagonist muscle MEP:IEMG ratio. No relationship was found between the amplitude of the antagonist H reflexes and the preceding antagonist IEMG. 5Five subjects showed an increase in the MEP:IEMG ratio preceding and during the initial part of the AG2 burst. 6Our method of analysis shows that changes in motor cortical excitability mediating the initiation of movement occur much closer to the onset of EMG activity (less than 23 ms) than the 80,100 ms lead time previously reported. The lack of such changes before the onset of the ANTAG burst suggests that this may be initiated by a different, perhaps subcortical, mechanism. [source]

The response of the coupled tropical ocean,atmosphere to westerly wind bursts

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 579 2002
Alexey V. Fedorov
Abstract Two different perspectives on El Niño are dominant in the literature: it is viewed either as one phase of a continual southern oscillation (SO), or alternatively as the transient response to the sudden onset of westerly wind bursts (WWBs). Occasionally those bursts do indeed have a substantial effect on the SO,the unusual strength of El Niño of 1997/98 appears to be related to a sequence of bursts,but frequently the bursts have little or no impact. What processes cause some bursts to be important, while others remain insignificant? The question is addressed by using a simple coupled tropical ocean,atmosphere model that simulates a continual, possibly attenuating, oscillation to study the response to WWBs. The results show that the impact of WWBs depends crucially on two factors: (i) the background state of the system as described by the mean depth of the thermocline and intensity of the mean winds, and (ii) the timing of the bursts with respect to the phase of the SO. Changes in the background conditions alter the sensitivity of the system, so that the impact of the bursts on El Niño may be larger during some decades than others. Changes in the timing of WWBs affect the magnitude and other characteristics of the SO by modifying the energetics of the ocean,atmosphere interactions. A reasonable analogy is a swinging pendulum subject to modest blows at random times,those blows can either magnify or diminish the amplitude, depending on their timing. It is demonstrated that a WWB can increase the strength of El Niño significantly, if it occurs 6 to 10 months before the peak of warming, or can reduce the intensity of the subsequent El Niño, if it occurs during the cold phase of the continual SO. Copyright © 2002 Royal Meteorological Society. [source]

On a cumulative damage process and resulting first passages times

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 1 2004
Waltraud Kahle
Abstract The reliability of a product is often affected by a damage process. In this paper we consider a shock model where at random times a shock causes a random damage. The cumulative damage process is assumed to be generated by a position-dependent marking of a doubly stochastic Poisson process. Some characteristics of this process are described. For general and special cases the probability that the damage process does not cross a certain threshold before a time t is calculated. Copyright © 2004 John Wiley & Sons, Ltd. [source]