Stochastic processes for finance

Stochastic Processes for Finance5 Contents Download free eBooks at bookboon.com Click on the ad to read more Increase your impact with MSM Executive Education For more information, visi

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Stochastic Processes for Finance

Download free books at

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Stochastic Processes for Finance

Patrick Roger Strasbourg University, EM Strasbourg Business School

June 2010

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Stochastic Processes for Finance Contents

Contents

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5

Contents

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Stochastic Processes for Finance Contents

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Stochastic Processes for Finance Introduction

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Stochastic Processes for Finance Discrete-time stochastic processes

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helping our global clients achieve high performance If this is your idea of a typical working day, then

Accenture is the place to be.

Turning a challenge into a learning curve.

Just another day at the office for a high performer.

Accenture Boot Camp – your toughest test yet

Visit accenture.com/bootcamp

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

 lim

m →+∞πm =

0.5 0.50.5 0.5





           

             

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2s

s

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How to retain your

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Stochastic Processes for Finance Continuous-time stochastic processes

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Stochastic Processes for Finance     Continuous-time stochastic processes

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

Zs+ (Zt− Zs)

FZ s



Zs

FZ s

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

Zt2

FZ s



− t

  

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

− EZs2

FZ s

+ 2ZsE

Zt



FZ s

+ 2Zs2− Z2

s − t

(Zt− Zs)2

+ Zs2 − t(t− s) + Zs2− t



exp (γZt)

FZ s



exp (γ(Zt− Zs)) exp(γZs)

FZ s



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= exp



2(t + s)2

1

√2πt

1

√2πt

= exp



2s2



= g(0, s)

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Increase your impact with MSM Executive Education

For almost 60 years Maastricht School of Management has been enhancing the management capacity

of professionals and organizations around the world through state-of-the-art management education Our broad range of Open Enrollment Executive Programs offers you a unique interactive, stimulating and

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Stochastic Processes for Finance Stochastic integral and Itô’s lemma

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ZT22

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With us you can

shape the future

Every single day

For more information go to:

www.eon-career.com

Your energy shapes the future.

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sds +

 t 0

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 t 0

ds +

 t 0

σdZs

= 

 t 0

ds + σ

 t 0

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2

∂2f

∂x2 [(Xt, t)dt + σ(Xt, t)dZt]2+1

∂2f

∂x2σ2(Xt, t)

dt+σ(Xt, t)∂f

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∂2g

∂x2σ2(Yt, t) = ∂g

∂xYt+

12

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Stochastic Processes for Finance       Stochastic integral and Itô’s lemma

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λsdZs− 1

2

 t 0

12

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It all starts at Boot Camp It’s 48 hours

that will stimulate your mind and

enhance your career prospects You’ll

packed with intellectual challenges and activities designed to let you discover what it really means to be a

and intense learning experience

It could be your toughest test yet, which is exactly what will make it

Choose Accenture for a career where the variety of opportunities and challenges allows you to make a

difference every day A place where you can develop your potential and grow professionally, working

alongside talented colleagues The only place where you can learn from our unrivalled experience, while

helping our global clients achieve high performance If this is your idea of a typical working day, then

Accenture is the place to be.

Turning a challenge into a learning curve.

Just another day at the office for a high performer.

Accenture Boot Camp – your toughest test yet

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σ2(Xt, t) dt < +∞ 

 X 

 t 0

 (Xs, s) ds +

 t 0

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       

Xtexp(−at) = c +

 t 0

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

 t 0

2

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Stochastic Processes for Finance Bibliography

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Stochastic Processes for Finance Bibliography

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stationary distribution, 20 transient, 19

no memory process, 48 process, 15, 48

Brownian motion, 59 transition matrix, 15 Martingale, 21, 49

Brownian motion, 59 Doob, 24

submartingale, 21, 49 super-martingale, 21, 49 Modi cation

stochastic process, 43 Novikov

condition, 89 Path, 40

càdlàg, 41 càglàd, 43 continuous, 40 Brownian motion, 58 LCRL, 43

nowhere differentiable, 59 RCLL, 41

Poisson distribution, 47 process, 47 Probability transition, 15 Snell envelope, 36 Stochastic differential equation, 91 linear, 93

solution conditions, 92

de nition, 91 Markov, 92 Stochastic integral, 71 calculation rules, 79 definition, 76 properties, 78 stochastic differential, 78 Download free eBooks at bookboon.com

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