Asymptotics for local maximal stack scores with general loop penalty function

Minimizing a General Penalty Function on a Single Machine via Developing Approximation Algorithms and FPTASs

This paper addresses the Tardy/Lost penalty minimization on a single machine. According to this penalty criterion, if the tardiness of a job exceeds a predefined value, the job will be lost and penalized by a fixed value. Besides its application in real world problems, Tardy/Lost measure is a general form for popular objective functions like weighted tardiness, late work and tardiness with reje...

A Local Maximal Function Simplifying Measure Differentiation

Di¤erentiation and absolute continuity are di¢ cult topics for students in a graduate integration course. We outline here a simpli…ed approach that has cut almost in half the time previously spent by the second author in covering these topics (as developed in chapter 5 of [7]); the time saved is used for a deeper discussion of Hilbert spaces and Fourier analysis. Our simpli…ed approach uses a l...

Weighted Norm Inequalities for the Local Sharp Maximal Function

Lecture 5 : Time speedup , General gap penalty function

If we believe that the two sequences x and y are similar then we might be able to optimally align them faster. For simplicity assume that m = n since our sequences are similar. If x and y align perfectly, then the optimal alignment corresponds to the diagonal in the dynamic programming table (now of size n × n). This is because all of the back pointers will be pointing diagonally. Therefore, if...

General Smile Asymptotics with Bounded Maturity

We provide explicit conditions on the distribution of risk-neutral log-returns which yield sharp asymptotic estimates on the implied volatility smile. We allow for a variety of asymptotic regimes, including both small maturity (with arbitrary strike) and extreme strike (with arbitrary bounded maturity), extending previous work of Benaim and Friz [Math. Finance, 19 (2009), pp. 1–12]. We present ...