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blackscholes model
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Martingales and stochastic integrals in the theory of continuous trading
Martingales and stochastic integrals in the theory of continuous trading,10.1016/03044149(81)900260,Stochastic Processes and Their Applications,J. M
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Martingales and stochastic integrals in the theory of continuous trading
(
Citations: 1056
)
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J. Michael Harrison
,
Stanley R. Pliska
This paper develops a general
stochastic model
of a frictionless security market with continuous trading. The vector price process is given by a semimartingale of a certain class, and the general
stochastic integral
is used to represent capital gains. Within the framework of this model, we discuss the modern theory of
contingent claim
valuation, including the celebrated
option pricing
formula of Black and Scholes. It is shown that the security market is complete if and only if its vector price process has a certain martingale representation property. A multidimensional generalization of the
BlackScholes model
is examined in some detail, and some other examples are discussed briefly.
Journal:
Stochastic Processes and Their Applications  STOCH PROC APPL
, vol. 11, no. 3, pp. 215260, 1981
DOI:
10.1016/03044149(81)900260
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Citation Context
(356)
...Using the second fundamental theorem of asset pricing (Harrison and Pliska
1981
), our economy may be incomplete with an infinite number of local martingale measures ℚ...
Robert A. Jarrow
,
et al.
A liquiditybased model for asset price bubbles
...Indeed, the fundamental theorem of asset pricing (Harrison and Pliska
1981
, Delbaen and Schachermayer
1994
) guarantees noarbitrage if an equivalent martingale measure exists, and completeness of the market if the equivalent martingale measure is unique...
Maria C. Mariani
,
et al.
Nonlinear problems modeling stochastic volatility and transaction cost...
...Mathematically, this implies the existence of an equivalent probability measure
Q
under which the process e
^{−rt }
S
_{ t }
is a martingale (eg, Harrison and Pliska
1981
and Shreve
2004
)...
Judith Glaser
,
et al.
Arbitragefree approximation of call price surfaces and input data ris...
...Harrison and Kreps (
1979
) and Harrison and Pliska (
1981
,
1983
) established the link between the absence of arbitrages and the concept of martingales...
Robert J. Elliott
,
et al.
Option Pricing and Filtering with Hidden MarkovModulated PureJump Pr...
...From the first fundamental theorem of asset pricing (Harrison and Kreps,
1979
; Harrison and Pliska,
1981
), the following riskneutral valuation formulas hold: and where
Massimiliano Barbi
.
On the riskneutral value of debt tax shields
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Citations
(1056)
Portfolios and risk premia for the long run
(
Citations: 2
)
Paolo Guasoni
,
Scott Robertson
Journal:
Annals of Applied Probability  ANN APPL PROBAB
, vol. 22, no. 2012, pp. 239284, 2012
A liquiditybased model for asset price bubbles
Robert A. Jarrow
,
Philip Protter
,
Alexandre F. Roch
Journal:
Quantitative Finance  QUANT FINANC
, vol. 12, no. 9, pp. 13391349, 2012
Nonlinear problems modeling stochastic volatility and transaction costs
Maria C. Mariani
,
Indranil SenGupta
Journal:
Quantitative Finance  QUANT FINANC
, vol. 12, no. 4, pp. 663670, 2012
Arbitragefree approximation of call price surfaces and input data risk
Judith Glaser
,
Pascal Heider
Journal:
Quantitative Finance  QUANT FINANC
, vol. 12, no. 1, pp. 6173, 2012
Option Pricing and Filtering with Hidden MarkovModulated PureJump Processes
Robert J. Elliott
,
Tak Kuen Siu
Journal:
Applied Mathematical Finance
, vol. aheadofp, no. aheadofp, pp. 125, 2012