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1
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Exponential martingales and CIR model

100%
Szatzschneider W.
Banach Center Publications
|
2008
|
tom 83
|
nr 1
243-249
EN
With the use of exponential martingales and the Girsanov theorem we show how to calculate bond prices in a large variety of square root processes. We clarify and correct several errors that abound in financial literature concerning these processes. The most important topics are linear risk premia, the Longstaff double square model, and calculations concerning correlated CIR processes.
2
Content available remote

Principal-agent approach to environmental improvements policies

63%
Szatzschneider W., Kwiatkowska T.
Banach Center Publications
|
2010
|
tom 90
|
nr 1
193-201
EN
Successful solution to any environmental problem implies working with Knightian uncertainty that explicitly deals with decision making under conditions of unstructured randomness. A 'wild' type of randomness that we will never discern due to its unstable properties makes the assignment of corresponding probabilities impossible. For that reason, the consideration of general economical factors within cost/benefit analysis must fail. So, instead of governmental intervention and a cup and trade scheme, we propose a direct financial market of certificates on environmental improvements. The approach is based on the Principal-Agent method. In this study we analyze the problem of one agent only, and take as example deforestation issues. In the analytical part we give examples how these certificates could be defined. We solve some optimization problems in well established stochastic models. The approximate knowledge which actions are environmentally friendly allows us to design good environmental certificates.
3
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Full cooperation applied to environmental improvements

51%
Jeanblanc M., Łochowski R., Szatzschneider W.
Banach Center Publications
|
2015
|
tom 104
|
nr 1
121-131
EN
We analyse the case of certificates of environmental improvements and full cooperation of two identical agents. We model pollution levels as geometric Brownian motions with quadratic costs of improvements. Our main result is the construction of the optimal improvements strategy in the case of separate actions, collusive actions and fusion. In certain range of the model parameters, the fusion solution generates lower pollution levels than separate and collusive actions.
4
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A version of the Harris-Spitzer "random constant velocity" model for infinite systems of particles

50%
Szatzschneider W.
Studia Mathematica
|
1978
|
tom 63
|
nr 2
171-187
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