Instituto para el desarrollo empresarial (INDEM)
http://hdl.handle.net/10016/6577
Sat, 21 Jan 2017 19:47:38 GMT2017-01-21T19:47:38ZInstituto para el desarrollo empresarial (INDEM)http://e-archivo.uc3m.es:80/bitstream/id/78556/LOGO INDEM_UCIII.jpg
http://hdl.handle.net/10016/6577
Differential equations connecting VaR and CVaR
http://hdl.handle.net/10016/24017
Differential equations connecting VaR and CVaR
Balbás, Alejandro; Balbás, Beatriz; Balbás, Raquel
Universidad Carlos III de Madrid. Instituto para el Desarrollo Empresarial
The Value at Risk (VaR) is a very important risk measure for practitioners, supervisors and researchers. Many practitioners draw on VaR as a critical instrument in Risk Management and other Actuarial/Financial problems, while super- visors and regulators must deal with VaR due to the Basel Accords and Solvency II, among other reasons. From a theoretical point of view VaR presents some drawbacks overcome by other risk measures such as the Conditional Value at Risk (CVaR). VaR is neither differentiable nor sub-additive because it is neither continuous nor convex. On the contrary, CVaR satis es all of these properties, and this simpli es many ana- lytical studies if VaR is replaced by CVaR. In this paper several differential equations connecting both VaR and CVaR will be presented. They will allow us to address several important issues involving VaR with the help of the CVaR properties. This new methodology seems to be very efficient. In particular, a new VaR Representation Theorem may be found, and optimization problems involving VaR or probabilistic constraints always have an equivalent differentiable optimization problem. Applications in VaR, marginal VaR, CVaR and marginal CVaR estimates will be addressed as well. An illustrative actuarial numerical example will be given.
Mon, 09 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10016/240172017-01-09T00:00:00ZThe newsvendor problem with convex risk
http://hdl.handle.net/10016/23950
The newsvendor problem with convex risk
Charron, Jean Philippe; Balbás, Alejandro
Universidad Carlos III de Madrid. Instituto para el Desarrollo Empresarial
The newsvendor problem is a classical topic in Management Science and Operations Research. It deals with purchases and price strategies when a least one deadline is involved. In this paper we will assume that the decision is driven by an optimization problem involving both expected pro ts and risks. As a main novelty, risks will be given by a convex risk measure, including the usual utility functions. This approach will allow us to nd necessary and su¢ cient optimality conditions under very general frameworks, since we will not need any speci c assumption about the demand distribution.
Mon, 12 Dec 2016 00:00:00 GMThttp://hdl.handle.net/10016/239502016-12-12T00:00:00ZMust an optimal buy and hold strategy contain any derivative?
http://hdl.handle.net/10016/23912
Must an optimal buy and hold strategy contain any derivative?
Balbás, Alejandro; Balbás, Beatriz; Balbás, Raquel
Universidad Carlos III de Madrid. Instituto para el Desarrollo Empresarial
Consider a portfolio choice problem maximizing the expected return and simultaneously minimizing a general (and frequently coherent) risk measure. This paper shows that every stock (or stock index) is often outperformed by a buy and hold strategy containing some of its derivatives and the underlying stock itself. As a consequence, every investment only containing international benchmarks will not be efficient, and the investors must properly add some derivatives. Though there is still a controversy, this finding had been pointed out in dynamic frameworks, but the novelty is that one does not need to rebalance the portfolio of derivatives before their expiration date. This is very important in practice because transaction costs are sometimes significant when trading derivatives.
Mon, 21 Nov 2016 00:00:00 GMThttp://hdl.handle.net/10016/239122016-11-21T00:00:00ZGood deal measurement in asset pricing: Actuarial and financial implications
http://hdl.handle.net/10016/23546
Good deal measurement in asset pricing: Actuarial and financial implications
Balbás, Alejandro; Garrido, José; Okhrati, Ramin
We will integrate in a single optimization problem a risk measure
beyond the variance and either arbitrage free real market quotations or financial pricing
rules generated by an arbitrage free stochastic pricing model. A sequence of investment
strategies such that the couple (risk; price) diverges to (-∞, -∞) will be called
good deal. We will see that good deals often exist in practice, and the paper main
objective will be to measure the good deal size. The provided good deal measures will
equal an optimal ratio between both risk and price, and there will exist alternative
interpretations of these measures. They will also provide the minimum relative (per
dollar) price modification that prevents the good deal existence. Moreover, they will
be a crucial instrument to detect those securities or marketed claims which are over
or under-priced. Many classical actuarial and financial optimization problems may
generate wrong solutions if the used market quotations or stochastic pricing models
do not prevent the good deal existence. This fact will be illustrated in the paper,
and it will be pointed out how the provided good deal measurement may be useful to
overcome this caveat. Numerical experiments will be yielded as well.
Mon, 12 Sep 2016 00:00:00 GMThttp://hdl.handle.net/10016/235462016-09-12T00:00:00Z