Heuristic optimisation in financial modelling

There is a large number of optimisation problems in theoretical and applied finance that are difficult to solve as they exhibit multiple local optima or are not ‘well-behaved’ in other ways (e.g., discontinuities in the objective function). One way to deal with such problems is to adjust and to simplify them, for instance by dropping constraints, until they can be solved with standard numerical methods. We argue that an alternative approach is the application of optimisation heuristics like Simulated Annealing or Genetic Algorithms. These methods have been shown to be capable of handling non-convex optimisation problems with all kinds of constraints. To motivate the use of such techniques in finance, we present several actual problems where classical methods fail. Next, several well-known heuristic techniques that may be deployed in such cases are described. Since such presentations are quite general, we then describe in some detail how a particular problem, portfolio selection, can be tackled by a particular heuristic method, Threshold Accepting. Finally, the stochastics of the solutions obtained from heuristics are discussed. We show, again for the example from portfolio selection, how this random character of the solutions can be exploited to inform the distribution of computations.     

Optimal control in a quantum cooling problem

The optimal control for cooling a quantum harmonic oscillator by controlling its frequency is considered. It is shown that this singular problem may be transformed with the proper choice of coordinates to an equivalent problem which is no longer singular. The coordinates used are sufficiently simple that a graphical solution is possible and eliminates the need to use a Weierstrass-like approach to show optimality. The optimal control of this problem is of significance in connection with cooling physical systems to low temperatures. It is also mathematically significant in showing the power and limitations of coordinate transformations for attacking apparently singular problems.     

Toward low-loss photonic crystal waveguides in InP/InGaAsP heterostructures

Line-defect photonic crystal waveguides exhibit severe propagation losses if they are implemented in semiconductor heterostructures with a weak refractive index contrast. We present, for what we believe is the first time, experimental structures for which we have evidence that fabrication imperfections are not the limiting factor in terms of propagation losses. We demonstrate a loss figure of 335±5 dB/cm, which is an improvement by a factor of about 2 with respect to state-of-the-art values. Simulations show that even lower losses can be obtained with different waveguide geometries. In other words, the dominant loss mechanism is related to the waveguide design, and losses are not expected to decrease upon further optimization of the fabrication process.     

Semiexperimental equilibrium structures for the equatorial conformers of N-methylpiperidone and tropinone by the mixed estimation method

N-Methylpiperidone (MPIP) and tropinone, which contain a structural motif found in numerous alkaloids, are too large to determine an accurate equilibrium structure either by ab initio methods or by experiment. However, the ground state rotational constants of the parent species and of all isotopologues with a substituted heavy atom ((13)C, (15)N, (18)O) are known from microwave spectroscopy. These constants have been corrected for the rovibrational contribution calculated from an ab initio cubic force field. These semiexperimental equilibrium rotational constants have been supplemented by carefully chosen structural parameters from medium level ab initio calculations. The two sets of data have been used in a weighted least-squares fit to determine reliable equilibrium structures for both molecules. This work shows that it is possible to determine reliable equilibrium structures for large molecules (34 degrees of freedom in the case of tropinone) at a detailed level of accuracy, and the method could be applied without too much difficulty to still larger molecules.     

Tautomeric and conformational properties of benzoylacetone, CH3-C(O)-CH2-C(O)-C6H5: gas-phase electron diffraction and quantum chemical study

Tautomeric and structural properties of benzoylacetone, CH(3)-C(O)-CH(2)-C(O)-C(6)H(5), have been studied by gas-phase electron diffraction (GED) and quantum chemical calculations (B3LYP and MP2 approximation with different basis sets up to aug-cc-pVTZ). Analysis of GED intensities resulted in the presence of 100% enol tautomer at 331(5) K. The existence of two possible enol conformers in about equal amounts is confirmed by both GED and quantum chemical results. In both conformers the enol ring possesses C(s) symmetry with a strongly asymmetric hydrogen bond. The experimental geometric parameters are reproduced very closely by the B3LYP/cc-pVTZ method.     

Top-down patterning of zeolitic imidazolate framework composite thin films by deep X-ray lithography

For the first time a top-down process was used to control the spatial location of Metal-Organic Frameworks on a surface. Deep X-ray lithography was utilised to micropattern a Zeolitic Imidazolate Framework layer on a sol-gel surface, with exposure hardening the sol-gel by inducing crosslinking while leaving the frameworks intact.     

Dynamical Mean-Field Equations for a Neural Network with Spike Timing Dependent Plasticity

We study the discrete dynamics of a fully connected network of threshold elements interacting via dynamically evolving synapses displaying spike timing dependent plasticity. Dynamical mean-field equations, which become exact in the thermodynamical limit, are derived to study the behavior of the system driven with uncorrelated and correlated Gaussian noise input. We use correlated noise to verify that our model gives account to the fact that correlated noise provides stronger drive for synaptic modification. Further we find that stochastic independent input leads to a noise dependent transition to the coherent state where all neurons fire together, most notably there exists an optimal noise level for the enhancement of synaptic potentiation in our model.     

Hydrophobin coated boehmite nanoparticles stabilizing oil in water emulsions

Hydrophobin coated boehmite nanoparticles have been used to establish tooth-paste like, homogenous emulsions. The surface-modified nanoparticles were simply obtained by mixing aqueous solutions of cationic boehmite particles with the anionic hydrophobin H Star Protein B® (HPB). Surface tension measurements clearly show that 1 wt.% boehmite binds up to 1 wt.% HPB. The strong interaction and aggregation of hydrophobin coated boehmite nanoparticles was proven by Cryo-TEM measurements, too. Interestingly, the combined use of 0.5 wt.% HPB and 0.5 wt.% boehmite as emulsifying agents resulted in very stable, homogenous, high internal phase emulsions (65 wt.% oil) that are stable over months. The established emulsions have also been characterized by rheological measurements. Storage moduli of more than 1000 Pa are characteristic for their high gel-like properties. Furthermore, light microscopy showed an average droplet size close to 1 μm with low polydispersity. Cryo-SEM confirmed that the hydrophobin coated nanoparticles are located at the interface of the oil droplets and therefore stabilize the emulsion systems.     

Novel Synthesis of 2‐Alkylquinolizinium‐1‐olates and Their 1,3‐Dipolar Cycloaddition Reactions with Acetylenes

Several 2‐alkylquinolizinium‐1‐olates 9 , i.e., heterobetaines, were prepared from ketone 11 , the latter being readily available either from pyridine‐2‐carbaldehyde via a Grignard reaction, followed by oxidation with MnO₂, or from 2‐picolinic acid (=pyridine‐2‐carboxylic acid) via the corresponding Weinreb amide and subsequent Grignard reaction. Mesoionic heterobetaines such as quinolizinium derivatives have the potential to undergo cycloaddition reactions with double and triple bonds, e.g., 1,3‐dipolar cycloadditions or Diels? Alder reactions. We here report on the scope and limitations of cycloaddition reactions of 2‐alkylquinolizinium‐1‐olates 9 with electron‐poor acetylene derivatives. As main products of the reaction, 5‐oxopyrrolo[2,1,5‐de]quinolizines (=‘[2.3.3]cyclazin‐5‐ones’) 19 were formed via a regioselective [2+3] cycloaddition, and cyclohexadienone derivatives, formed via a Diels? Alder reaction, were obtained as side products. The structures of 2‐benzylquinolizinium‐1‐olate ( 9a ) and two ‘[2.3.3]cyclazin‐5‐ones’ 19i and 19l were established by X‐ray crystallography.     

Unexpected Course of the Reaction of 2‐Unsubstituted 1H‐Imidazole 3‐Oxides with Ethyl Acrylate

The attempted ethenylation at C(2) of 2‐unsubstituted 1H‐imidazole N‐oxides with ethyl acrylate (=prop‐2‐enoate) in the presence of Pd(OAc)₂ does not occur. In contrast to the other aromatic N‐oxides, the [2+3] cycloaddition of imidazole N‐oxides predominates, and 3‐hydroxyacrylates, isomeric with the cycloadducts, are key products for the subsequent reaction. The final products were identified as dehydrated 2+1 adducts of 1H‐imidazole N‐oxide and ethyl acrylate. The role of the catalyst is limited to the dehydration of the intermediate 3‐hydroxypropanoates to give 1H‐imidazol‐2‐yl‐substituted acrylates.