Closed-form Transformations from Risk-neutral to Real-world Distributions

2004 ◽  
Author(s):  
Xiaoquan Liu ◽  
Mark B. Shackleton ◽  
Stephen J. Taylor ◽  
Xinzhong Xinzhong Xu
Keyword(s):  
Closed Form ◽  
Real World ◽  
Risk Neutral

Closed-form transformations from risk-neutral to real-world distributions

2007 ◽  
Vol 31 (5) ◽  
pp. 1501-1520 ◽  
Author(s):  
Xiaoquan Liu ◽  
Mark B. Shackleton ◽  
Stephen J. Taylor ◽  
Xinzhong Xu
Keyword(s):  
Closed Form ◽  
Real World ◽  
Risk Neutral

scholarly journals A NOTE ON REAL-WORLD AND RISK-NEUTRAL DYNAMICS FOR HEATH–JARROW–MORTON FRAMEWORKS

2020 ◽  
Vol 23 (03) ◽  
pp. 2050020
Author(s):  
DAVID CRIENS
Keyword(s):  
Brownian Motion ◽  
Real World ◽  
Random Measure ◽  
Jump Condition ◽  
Poisson Random Measure ◽  
Change Of Measure ◽  
The Real ◽  
Infinite Dimensional ◽  
Risk Neutral ◽  
Equivalent Change Of Measure

We show that for time-inhomogeneous Markovian Heath–Jarrow–Morton models driven by an infinite-dimensional Brownian motion and a Poisson random measure an equivalent change of measure exists whenever the real-world and the risk-neutral dynamics can be defined uniquely and are related via a drift and a jump condition.

A Closed-Form Solution for Selecting Maximum Critically Damped Actuator Impedance Parameters

2014 ◽  
Vol 137 (4) ◽  
Author(s):  
Nicholas Paine ◽  
Luis Sentis
Keyword(s):  
Closed Form ◽  
Parameter Space ◽  
Real World ◽  
Closed Form Solution ◽  
System Stability ◽  
Limiting Factors ◽  
Closed Form Expression ◽  
Phase Margin ◽  
Form Expression ◽  
Feedback Parameter

This paper introduces a simple and effective method for selecting the maximum feedback gains in PD-type controllers applied to actuators where feedback delay and derivative signal filtering are present. The method provides the maximum feedback parameters that satisfy a phase margin criteria, producing a closed-loop system with high stability and a dynamic response with near-minimum settling time. Our approach is unique in that it simultaneously possesses: (1) a model of real-world performance-limiting factors (i.e., filtering and delay), (2) the ability to meet performance and stability criteria, and (3) the simplicity of a single closed-form expression. A central focus of our approach is the characterization of system stability through exhaustive searches of the feedback parameter space. Using this search-based method, we locate a set of maximum feedback parameters based on a phase margin criteria. We then fit continuous equations to this data and obtain a closed-form expression which matches the sampled data to within 2–4% error for the majority of the parameter space. We apply our feedback parameter selection method to two real-world actuators with widely differing system properties and show that our method successfully produces the maximum achievable nonoscillating impedance response.

scholarly journals Exact Time-Dependent Queue-Length Solution to a Discrete-Time Geo/D/1 Queue

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 717
Author(s):  
Jung Woo Baek ◽  
Yun Han Bae
Keyword(s):  
Closed Form ◽  
Discrete Time ◽  
Real World ◽  
Queue Length ◽  
Service Systems ◽  
Time Dependent ◽  
World Systems ◽  
Exact Time ◽  
Queuing Models

Time-dependent solutions to queuing models are beneficial for evaluating the performance of real-world systems such as communication, transportation, and service systems. However, restricted results have been reported due to mathematical complexity. In this study, we present a time-dependent queue-length formula for a discrete-time G e o / D / 1 queue starting with a positive number of initial customers. We derive the time-dependent formula in closed form.

A class of complete benchmark models with intensity-based jumps

2004 ◽  
Vol 41 (1) ◽  
pp. 19-34 ◽  
Author(s):  
Eckhard Platen
Keyword(s):  
Probability Measure ◽  
Financial Market ◽  
Real World ◽  
Present Value ◽  
Market Models ◽  
Growth Optimal Portfolio ◽  
Conditional Expectations ◽  
Risk Neutral ◽  
Security Price ◽  
Value Pricing

This paper proposes a class of complete financial market models, the benchmark models, with security price processes that exhibit intensity-based jumps. The benchmark or reference unit is chosen to be the growth-optimal portfolio. Primary security account prices, when expressed in units of the benchmark, turn out to be local martingales. In the proposed framework an equivalent risk-neutral measure need not exist. Benchmarked fair derivative prices are obtained as conditional expectations of future benchmarked prices under the real-world probability measure. This concept of fair pricing generalizes the classical risk-neutral approach and the actuarial present-value pricing methodology.

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