Mathematical Finance in Discrete Time

2004 ◽  
pp. 101-151
Author(s):  
Nicholas H. Bingham ◽  
Rüdiger Kiesel
Keyword(s):  
Discrete Time ◽  
Mathematical Finance

Mathematical Finance in Discrete Time

1998 ◽  
pp. 83-131
Author(s):  
Nicholas H. Bingham ◽  
Rüdiger Kiesel
Keyword(s):  
Discrete Time ◽  
Mathematical Finance

scholarly journals Asymptotics for the discrete-time average of the geometric Brownian motion and Asian options

2017 ◽  
Vol 49 (2) ◽  
pp. 446-480 ◽  
Author(s):  
Dan Pirjol ◽  
Lingjiong Zhu
Keyword(s):  
Brownian Motion ◽  
Discrete Time ◽  
Moment Generating Function ◽  
Mathematical Finance ◽  
Geometric Brownian Motion ◽  
Time Averaging ◽  
Asian Options ◽  
Time Average ◽  
Averaging Time ◽  
The Moment

Abstract The time average of geometric Brownian motion plays a crucial role in the pricing of Asian options in mathematical finance. In this paper we consider the asymptotics of the discrete-time average of a geometric Brownian motion sampled on uniformly spaced times in the limit of a very large number of averaging time steps. We derive almost sure limit, fluctuations, large deviations, and also the asymptotics of the moment generating function of the average. Based on these results, we derive the asymptotics for the price of Asian options with discrete-time averaging in the Black–Scholes model, with both fixed and floating strike.

The Effect of Partly Missing Covariates on Statistical Power in Randomized Controlled Trials With Discrete-Time Survival Endpoints

Methodology ◽  
2017 ◽  
Vol 13 (2) ◽  
pp. 41-60
Author(s):  
Shahab Jolani ◽  
Maryam Safarkhani
Keyword(s):  
Randomized Controlled Trials ◽  
Discrete Time ◽  
Treatment Effect ◽  
Survival Data ◽  
Controlled Trials ◽  
Missing Covariates ◽  
Indicator Method ◽  
Imputation Methods ◽  
Randomized Controlled ◽  
Baseline Covariates

Abstract. In randomized controlled trials (RCTs), a common strategy to increase power to detect a treatment effect is adjustment for baseline covariates. However, adjustment with partly missing covariates, where complete cases are only used, is inefficient. We consider different alternatives in trials with discrete-time survival data, where subjects are measured in discrete-time intervals while they may experience an event at any point in time. The results of a Monte Carlo simulation study, as well as a case study of randomized trials in smokers with attention deficit hyperactivity disorder (ADHD), indicated that single and multiple imputation methods outperform the other methods and increase precision in estimating the treatment effect. Missing indicator method, which uses a dummy variable in the statistical model to indicate whether the value for that variable is missing and sets the same value to all missing values, is comparable to imputation methods. Nevertheless, the power level to detect the treatment effect based on missing indicator method is marginally lower than the imputation methods, particularly when the missingness depends on the outcome. In conclusion, it appears that imputation of partly missing (baseline) covariates should be preferred in the analysis of discrete-time survival data.

Discrete-Time Delay Dynamics of Boundedly Rational Monopoly

2012 ◽  
Author(s):  
Akio Matsumato ◽  
Ferenc Szidarovsky
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Discrete Time Delay

DECOMPOSITION OF NONLINEAR DISCRETE-TIME STOCHASTIC SYSTEMS

1985 ◽  
Vol 5 (4) ◽  
pp. 399-413
Author(s):  
Chongzhao Han
Keyword(s):  
Discrete Time ◽  
Stochastic Systems
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