DEE - Artículos de Revistas
http://hdl.handle.net/10016/715
2014-09-20T20:02:47ZGood deals in markets with friction
http://hdl.handle.net/10016/18157
Good deals in markets with friction
Balbás, Alejandro; Balbás, Beatriz; Balbás, Raquel
This paper studies an optimization problem involving pay-offs of (perhaps dynamic) investment
strategies. The pay-off is the decision variable, the expected pay-off is maximized and its risk is
minimized. The pricing rule may incorporate transaction costs and the risk measure is continuous,
coherent and expectation bounded.We will prove the necessity of dealing with pricing rules such that
there exists an essentially bounded stochastic discount factor that must also be bounded from below
by a strictly positive value. Otherwise, good deals will be available to traders, i.e. depending on the
selected risk measure, investors can choose pay-offs whose (risk, return) will be as close as desired
to (−1,1) or (−1,1). This pathological property still holds for vector risk measures (i.e. if we
minimize a vector-valued function whose components are risk measures). It is worth pointing out that,
essentially, bounded stochastic discount factors are not usual in the financial literature. In particular,
the most famous frictionless, complete and arbitrage-free pricing models imply the existence of good
deals for every continuous, coherent and expectation bounded (scalar or vector) measure of risk, and
the incorporation of transaction costs will not guarantee the solution of this caveat
2013-06-01T00:00:00ZVector Risk Functions
http://hdl.handle.net/10016/18155
Vector Risk Functions
Balbás, Alejandro; Balbás, Raquel; Jiménez Guerra, Pedro
The paper introduces a new notion of vector-valued risk function, a crucial notion in Actuarial and Financial Mathematics. Both deviations and expectation bounded or coherent risk measures are defined and analyzed. The relationships with both scalar and vector risk functions of previous literature are discussed, and it is pointed out that this new approach seems to appropriately integrate several preceding points of view. The framework of the study is the general setting of Banach lattices and Bochner integrable vector-valued random variables. Sub-gradient linked representation theorems and practical examples are provided.
2012-11-01T00:00:00ZCompatibility between pricing rules and risk measures: the CCVaR
http://hdl.handle.net/10016/18153
Compatibility between pricing rules and risk measures: the CCVaR
Balbás, Alejandro; Balbás, Raquel
This paper has considered a risk measure? and a (maybe incomplete and/or imperfect) arbitrage-free market with pricing rule p. They are said to be compatible if there are no reachable strategies y such that p (y) remains bounded and ?(y) is close to - 8. We show that the lack of compatibility leads to meaningless situations in financial or actuarial applications. The presence of compatibility is characterized by properties connecting the Stochastic Discount Factor of p and the sub-gradient of ?. Consequently, several examples pointing out that the lack of compatibility may occur in very important pricing models are yielded. For instance the CVaR and the DPT are not compatible with the Black and Scholes model or the CAPM. We prove that for a given incompatible couple (p,?) we can construct a minimal risk measure ?p compatible with p and such that ?p = ? . This result is particularized for the CVaR and the CAPM and the Black and Scholes model. Therefore we construct the Compatible Conditional Value at Risk (CCVaR). It seems that the CCVaR preserves the good properties of the CVaR and overcomes its shortcomings.
2009-06-01T00:00:00ZMartingales and Arbitrage: a new look
http://hdl.handle.net/10016/18152
Martingales and Arbitrage: a new look
Balbás, Alejandro; Jimenez Guerra, Pedro
This paper addresses the equivalence between the absence of arbitrage and the existence of equivalent martingale measures. The equivalence will be established under quite weak assumptions since there are no conditions on the set of trading dates (it may be finite or countable, with bounded or unbounded horizon, etc.) or on the trajectories of the price process (for instance, they do not have to be right-continuous). Besides we will deal with arbitrage portfolios rather than free-lunches. The concept of arbitrage is much more intuitive than the concept of free lunch and has more clear economic interpretation. Furthermore it is more easily tested in theoretical models or practical applications. In order to overcome the usual mathematical difficulties arising when dealing with arbitrage strategies, the set of states of nature will be widened by drawing on projective systems of Radon probability measures, whose projective limit will be the martingale measure. The existence of densities between the "real" probabilities and the "risk-neutral" probabilities will be guaranteed by introducing the concept of "projective equivalence". Hence some classical counter-examples will be solved and a complete characterization of the absence of arbitrage will be provided in a very general framework.
2009-06-01T00:00:00Z